 6.6.5.1: An ordered pair is a ________ of an inequality in and when the ineq...
 6.6.2.1: The first step in solving a system of equations by the method of __...
 6.6.6.1: In the process called ________, you find the maximum or minimum val...
 6.6.3.1: A system of equations in ________ form has a stairstep pattern wit...
 6.1: Exercises 110, solve the system by the method of substitution. x y ...
 6.6.4.1: The process of writing a rational expression as the sum of two or m...
 6.6.1.1: A ________ of a system of equations is an ordered pair that satisfi...
 6.6.5.2: The ________ of an inequality is the collection of all solutions of...
 6.6.2.2: Two systems of equations that have the same solution set are called...
 6.6.6.2: One type of optimization strategy is called ________ ________.
 6.6.3.2: A solution of a system of three linear equations in three unknowns ...
 6.2: Exercises 110, solve the system by the method of substitution. 2xx3...
 6.6.4.2: If the degree of the numerator of a rational expression is greater ...
 6.6.1.2: The first step in solving a system of equations by the method of __...
 6.6.5.3: A ________ of a system of inequalities in and is a point that satis...
 6.6.2.3: A system of linear equations that has at least one solution is call...
 6.6.6.3: The ________ function of a linear programming problem gives the qua...
 6.6.3.3: The process used to write a system of linear equations in rowechel...
 6.3: Exercises 110, solve the system by the method of substitution.4x8xy...
 6.6.4.3: Each fraction on the right side of the equation is a ________ _____...
 6.6.1.3: Graphically, the solution of a system of two equations is the _____...
 6.6.5.4: A ________ ________ of a system of inequalities in two variables is...
 6.6.2.4: In business applications, the ________ ________ is defined as the p...
 6.6.6.4: The ________ of a linear programming problem determine the set of _...
 6.6.3.4: Interchanging two equations of a system of linear equations is a __...
 6.4: Exercises 110, solve the system by the method of substitution. 0xx6...
 6.6.4.4: You obtain the ________ ________ after multiplying each side of the...
 6.6.1.4: In business applications, the point at which the revenue equals cos...
 6.6.5.5: In Exercises 518, sketch the graph of the inequality. y < 5 x 2 x <...
 6.6.2.5: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.5: The feasible solutions are ________ or ________ the boundary of the...
 6.6.3.5: A system of equations is called ________ when the number of equatio...
 6.5: Exercises 110, solve the system by the method of substitution.0.5x1...
 6.6.4.5: In Exercises 58, match the rational expression with the form of its...
 6.6.1.5: In Exercises 5 and 6, determine whether each ordered pair is a solu...
 6.6.5.6: In Exercises 518, sketch the graph of the inequality. y y < 5 x 2 x...
 6.6.2.6: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.6: If a linear programming problem has a solution, then it must occur ...
 6.6.3.6: The equation is called the ________ equation, and it models the hei...
 6.6: Exercises 110, solve the system by the method of substitution. xx25...
 6.6.4.6: In Exercises 58, match the rational expression with the form of its...
 6.6.1.6: In Exercises 5 and 6, determine whether each ordered pair is a solu...
 6.6.5.7: In Exercises 518, sketch the graph of the inequality. x 6
 6.6.2.7: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.7: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.7: In Exercises 710, determine whether each ordered triple is a soluti...
 6.7: Exercises 110, solve the system by the method of substitution.x2 y2...
 6.6.4.7: In Exercises 58, match the rational expression with the form of its...
 6.6.1.7: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.8: In Exercises 518, sketch the graph of the inequality. x < 4
 6.6.2.8: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.8: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.8: In Exercises 710, determine whether each ordered triple is a soluti...
 6.8: Exercises 110, solve the system by the method of substitution.x2 y2...
 6.6.4.8: In Exercises 58, match the rational expression with the form of its...
 6.6.1.8: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.9: In Exercises 518, sketch the graph of the inequality. y > 7 1
 6.6.2.9: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.9: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.9: In Exercises 710, determine whether each ordered triple is a soluti...
 6.9: Exercises 110, solve the system by the method of substitution. y 2x...
 6.6.4.9: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.9: In Exercises 714, solve the system by the method of substitution. C...
 6.6.1.10: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.10: In Exercises 518, sketch the graph of the inequality. 10 y
 6.6.2.10: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.10: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.10: In Exercises 710, determine whether each ordered triple is a soluti...
 6.10: Exercises 110, solve the system by the method of substitution. x y ...
 6.6.4.10: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.11: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.11: In Exercises 518, sketch the graph of the inequality. y < 2 x
 6.6.2.11: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.11: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.11: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.11: In Exercises 1114, solve the system graphically. 2x y x 5y 106
 6.6.4.11: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.12: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.12: In Exercises 518, sketch the graph of the inequality. y > 4x 3
 6.6.2.12: In Exercises 512, solve the system by the method of elimination. La...
 6.6.6.12: In Exercises 712, find the minimum and maximum values of the object...
 6.6.3.12: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.12: In Exercises 1114, solve the system graphically. 8x2x3y5y328
 6.6.4.12: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.13: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.13: In Exercises 518, sketch the graph of the inequality. 2y x 4
 6.6.2.13: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.13: In Exercises 1316, sketch the region determined by the constraints....
 6.6.3.13: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.13: In Exercises 1114, solve the system graphically. y y 2x2 4x 1x2 4x 38
 6.6.4.13: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.14: In Exercises 714, solve the system by the method of substitution. C...
 6.6.5.14: In Exercises 518, sketch the graph of the inequality. 5x 3y 15
 6.6.2.14: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.14: In Exercises 1316, sketch the region determined by the constraints....
 6.6.3.14: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.14: In Exercises 1114, solve the system graphically.y2 2y x 0x y 0
 6.6.4.14: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.15: In Exercises 1524, solve the system by the method of substitution x...
 6.6.5.15: In Exercises 518, sketch the graph of the inequality. x 12 y 22 < 9...
 6.6.2.15: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.15: In Exercises 1316, sketch the region determined by the constraints....
 6.6.3.15: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.15: In Exercises 1518, use a graphing utility to solve the systems of e...
 6.6.4.15: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.16: In Exercises 1524, solve the system by the method of substitution x...
 6.6.5.16: In Exercises 518, sketch the graph of the inequality. x 12 y 42 > 9...
 6.6.2.16: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.16: In Exercises 1316, sketch the region determined by the constraints....
 6.6.3.16: In Exercises 1116, use backsubstitution to solve the system of lin...
 6.16: In Exercises 1518, use a graphing utility to solve the systems of e...
 6.6.4.16: In Exercises 916, write the form of the partial fraction decomposit...
 6.6.1.17: In Exercises 1524, solve the system by the method of substitution 2...
 6.6.5.17: In Exercises 518, sketch the graph of the inequality. y 11 x 2
 6.6.2.17: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.17: In Exercises 1720, use a graphing utility to graph the region deter...
 6.6.3.17: In Exercises 17 and 18, perform the row operation and write the equ...
 6.17: In Exercises 1518, use a graphing utility to solve the systems of e...
 6.6.4.17: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.18: In Exercises 1524, solve the system by the method of substitution 6...
 6.6.5.18: In Exercises 518, sketch the graph of the inequality. y > 15x2 x 4 y
 6.6.2.18: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.18: In Exercises 1720, use a graphing utility to graph the region deter...
 6.6.3.18: In Exercises 17 and 18, perform the row operation and write the equ...
 6.18: In Exercises 1518, use a graphing utility to solve the systems of e...
 6.6.4.18: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.19: In Exercises 1524, solve the system by the method of substitution 1...
 6.6.5.19: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.19: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.19: In Exercises 1720, use a graphing utility to graph the region deter...
 6.6.3.19: In Exercises 1924, solve the system of linear equations and check a...
 6.19: Body Mass Index (BMI) is a measure of body fat based on height and ...
 6.6.4.19: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.20: In Exercises 1524, solve the system by the method of substitution 0...
 6.6.5.20: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.20: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.20: In Exercises 1720, use a graphing utility to graph the region deter...
 6.6.3.20: In Exercises 1924, solve the system of linear equations and check a...
 6.20: Choice of Two Jobs You receive two sales job offers. One company of...
 6.6.4.20: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.21: In Exercises 1524, solve the system by the method of substitution 1...
 6.6.5.21: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.21: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.21: In Exercises 2124, find the minimum and maximum values of the objec...
 6.6.3.21: In Exercises 1924, solve the system of linear equations and check a...
 6.21: Geometry The perimeter of a rectangle is 68 feet and its width is t...
 6.6.4.21: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.22: In Exercises 1524, solve the system by the method of substitution 1...
 6.6.5.22: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.22: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.22: In Exercises 2124, find the minimum and maximum values of the objec...
 6.6.3.22: In Exercises 1924, solve the system of linear equations and check a...
 6.22: Geometry The perimeter of a rectangle is 40 inches. The area of the...
 6.6.4.22: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.23: In Exercises 1524, solve the system by the method of substitution 6...
 6.6.5.23: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.23: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.23: In Exercises 2124, find the minimum and maximum values of the objec...
 6.6.3.23: In Exercises 1924, solve the system of linear equations and check a...
 6.23: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.23: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.24: In Exercises 1524, solve the system by the method of substitution 2...
 6.6.5.24: In Exercises 1928, use a graphing utility to graph the inequality y...
 6.6.2.24: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.24: In Exercises 2124, find the minimum and maximum values of the objec...
 6.6.3.24: In Exercises 1924, solve the system of linear equations and check a...
 6.24: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.24: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.25: In Exercises 2528, you are given the total annual interest earned f...
 6.6.5.25: In Exercises 1928, use a graphing utility to graph the inequality x...
 6.6.2.25: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.25: In Exercises 2528, find the minimum and maximum values of the objec...
 6.6.3.25: In Exercises 2546, solve the system of linear equations and check a...
 6.25: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.25: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.26: In Exercises 2528, you are given the total annual interest earned f...
 6.6.5.26: In Exercises 1928, use a graphing utility to graph the inequality 2...
 6.6.2.26: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.26: In Exercises 2528, find the minimum and maximum values of the objec...
 6.6.3.26: In Exercises 2546, solve the system of linear equations and check a...
 6.26: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.26: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.27: In Exercises 2528, you are given the total annual interest earned f...
 6.6.5.27: In Exercises 1928, use a graphing utility to graph the inequality 2...
 6.6.2.27: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.27: In Exercises 2528, find the minimum and maximum values of the objec...
 6.6.3.27: In Exercises 2546, solve the system of linear equations and check a...
 6.27: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.27: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.28: In Exercises 2528, you are given the total annual interest earned f...
 6.6.5.28: In Exercises 1928, use a graphing utility to graph the inequality 1...
 6.6.2.28: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.28: In Exercises 2528, find the minimum and maximum values of the objec...
 6.6.3.28: In Exercises 2546, solve the system of linear equations and check a...
 6.28: In Exercises 2328, solve the system by the method of elimination an...
 6.6.4.28: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.29: In Exercises 2932, solve the system by the method of substitution x...
 6.6.5.29: In Exercises 2932, write an inequality for the shaded region shown ...
 6.6.2.29: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.29: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.29: In Exercises 2546, solve the system of linear equations and check a...
 6.29: In Exercises 2932, match the system of linear equations with its gr...
 6.6.4.29: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.30: In Exercises 2932, solve the system by the method of substitution x...
 6.6.5.30: In Exercises 2932, write an inequality for the shaded region shown ...
 6.6.2.30: In Exercises 1330, solve the system by the method of elimination an...
 6.6.6.30: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.30: In Exercises 2546, solve the system of linear equations and check a...
 6.30: In Exercises 2932, match the system of linear equations with its gr...
 6.6.4.30: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.31: In Exercises 2932, solve the system by the method of substitution x...
 6.6.5.31: In Exercises 2932, write an inequality for the shaded region shown ...
 6.6.2.31: In Exercises 3134, match the system of linear equations with its gr...
 6.6.6.31: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.31: In Exercises 2546, solve the system of linear equations and check a...
 6.31: In Exercises 2932, match the system of linear equations with its gr...
 6.6.4.31: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.32: In Exercises 2932, solve the system by the method of substitution y...
 6.6.5.32: In Exercises 2932, write an inequality for the shaded region shown ...
 6.6.2.32: In Exercises 3134, match the system of linear equations with its gr...
 6.6.6.32: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.32: In Exercises 2546, solve the system of linear equations and check a...
 6.32: In Exercises 2932, match the system of linear equations with its gr...
 6.6.4.32: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.33: In Exercises 3344, solve the system graphically. x3x2yy220
 6.6.5.33: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.33: In Exercises 3134, match the system of linear equations with its gr...
 6.6.6.33: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.33: In Exercises 2546, solve the system of linear equations and check a...
 6.33: In Exercises 33 and 34, find the equilibrium point of the demand an...
 6.6.4.33: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.34: In Exercises 3344, solve the system graphically. x3xy2y05x
 6.6.5.34: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.34: In Exercises 3134, match the system of linear equations with its gr...
 6.6.6.34: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.34: In Exercises 2546, solve the system of linear equations and check a...
 6.34: In Exercises 33 and 34, find the equilibrium point of the demand an...
 6.6.4.34: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.35: In Exercises 3344, solve the system graphically. x5x3y3y36
 6.6.5.35: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.35: In Exercises 3540, use any method to solve the system. 3x 5y 72x y 97x
 6.6.6.35: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.35: In Exercises 2546, solve the system of linear equations and check a...
 6.35: In Exercises 3538, use backsubstitution to solve the system of lin...
 6.6.4.35: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.36: In Exercises 3344, solve the system graphically. xx2yy72x
 6.6.5.36: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.36: In Exercises 3540, use any method to solve the system. x 3y 174x 3y 73
 6.6.6.36: In Exercises 2936, the linear programming problem has an unusual ch...
 6.6.3.36: In Exercises 2546, solve the system of linear equations and check a...
 6.36: In Exercises 3538, use backsubstitution to solve the system of lin...
 6.6.4.36: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.37: In Exercises 3344, solve the system graphically. x y 4x2 y2 4x 0
 6.6.5.37: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.37: In Exercises 3540, use any method to solve the system. y 2x 5y 5x 11
 6.6.6.37: Optimal Profit A merchant plans to sell two models of MP3 players a...
 6.6.3.37: In Exercises 2546, solve the system of linear equations and check a...
 6.37: In Exercises 3538, use backsubstitution to solve the system of lin...
 6.6.4.37: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.38: In Exercises 3344, solve the system graphically. x y 3x2 6x 27 y2 0 x
 6.6.5.38: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.38: In Exercises 3540, use any method to solve the system. 7x 3y 16y x 2
 6.6.6.38: Optimal Profit A manufacturer produces two models of elliptical cro...
 6.6.3.38: In Exercises 2546, solve the system of linear equations and check a...
 6.38: In Exercises 3538, use backsubstitution to solve the system of lin...
 6.6.4.38: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.39: In Exercises 3344, solve the system graphically. x y 3 0x2 4x 7 yx
 6.6.5.39: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.39: In Exercises 3540, use any method to solve the system. x 5y 216x 5y 21
 6.6.6.39: Optimal Cost An animal shelter mixes two brands of dry dog food. Br...
 6.6.3.39: In Exercises 2546, solve the system of linear equations and check a...
 6.39: In Exercises 3942, use Gaussian elimination to solve the system of ...
 6.6.4.39: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.40: In Exercises 3344, solve the system graphically. y2 4x 1112 x y012 x y
 6.6.5.40: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.40: In Exercises 3540, use any method to solve the system. 4x 3y 65x 7y...
 6.6.6.40: Optimal Cost A humanitarian agency can use two models of vehicles f...
 6.6.3.40: In Exercises 2546, solve the system of linear equations and check a...
 6.40: In Exercises 3942, use Gaussian elimination to solve the system of ...
 6.6.4.40: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.41: In Exercises 3344, solve the system graphically. 3x 2y 0x2 y2 4
 6.6.5.41: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.41: Airplane Speed An airplane flying into a headwind travels the 1800...
 6.6.6.41: Optimal Revenue An accounting firm has 780 hours of staff time and ...
 6.6.3.41: In Exercises 2546, solve the system of linear equations and check a...
 6.41: In Exercises 3942, use Gaussian elimination to solve the system of ...
 6.6.4.41: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.1.42: In Exercises 3344, solve the system graphically. 2x y 3 0x2 y2 4x 0 3
 6.6.5.42: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.42: Airplane Speed Two planes start from Los Angeles International Airp...
 6.6.6.42: Optimal Revenue The accounting firm in Exercise 41 lowers its charg...
 6.6.3.42: In Exercises 2546, solve the system of linear equations and check a...
 6.42: In Exercises 3942, use Gaussian elimination to solve the system of ...
 6.6.4.42: In Exercises 1742, write the partial fraction decomposition of the ...
 6.6.4.43: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.43: In Exercises 3344, solve the system graphically. x23x2y216y25 0
 6.6.5.43: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.43: Nutrition Two cheeseburgers and one small order of French fries fro...
 6.6.6.43: A fruit grower raises crops A and B. The yield is 300 bushels per a...
 6.6.3.43: In Exercises 2546, solve the system of linear equations and check a...
 6.43: In Exercises 43 and 44, solve the nonsquare system of equations. 5x...
 6.6.4.44: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.44: In Exercises 3344, solve the system graphically. x2 y2 25x 82 y2 41 x
 6.6.5.44: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.44: Nutrition One eightounce glass of apple juice and one eightounce ...
 6.6.6.44: Optimal Profit In Exercise 43, the profit is $185 per acre for crop...
 6.6.3.44: In Exercises 2546, solve the system of linear equations and check a...
 6.44: In Exercises 43 and 44, solve the nonsquare system of equations. 2x...
 6.6.4.45: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.45: In Exercises 4548, use a graphing utility to solve the system of eq...
 6.6.5.45: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.45: In Exercises 4548, find the equilibrium point of the demand and sup...
 6.6.6.45: Media Selection A company has budgeted a maximum of $1,000,000 for ...
 6.6.3.45: In Exercises 2546, solve the system of linear equations and check a...
 6.45: In Exercises 45 and 46, find the equation of the parabola that pass...
 6.6.4.46: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.46: In Exercises 4548, use a graphing utility to solve the system of eq...
 6.6.5.46: In Exercises 3346, sketch the graph (and label the vertices) of the...
 6.6.2.46: In Exercises 4548, find the equilibrium point of the demand and sup...
 6.6.6.46: Investment Portfolio An investor has up to $450,000 to invest in tw...
 6.6.3.46: In Exercises 2546, solve the system of linear equations and check a...
 6.46: In Exercises 45 and 46, find the equation of the parabola that pass...
 6.6.4.47: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.47: In Exercises 4548, use a graphing utility to solve the system of eq...
 6.6.5.47: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.47: In Exercises 4548, find the equilibrium point of the demand and sup...
 6.6.6.47: In Exercises 4749, determine whether the statement is true or false...
 6.6.3.47: In Exercises 47 and 48, an object moving vertically is at the given...
 6.47: In Exercises 47 and 48, find the equation of the circle that passes...
 6.6.4.48: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.48: In Exercises 4548, use a graphing utility to solve the system of eq...
 6.6.5.48: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.48: In Exercises 4548, find the equilibrium point of the demand and sup...
 6.6.6.48: In Exercises 4749, determine whether the statement is true or false...
 6.6.3.48: In Exercises 47 and 48, an object moving vertically is at the given...
 6.48: In Exercises 47 and 48, find the equation of the circle that passes...
 6.6.4.49: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.49: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.49: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.49: Acid Mixture Thirty liters of a 40% acid solution is obtained by mi...
 6.6.6.49: In Exercises 4749, determine whether the statement is true or false...
 6.6.3.49: In Exercises 4954, find the equation of the parabola that passes th...
 6.49: Data Analysis: ECommerce The table shows the retail ecommerce sal...
 6.6.4.50: In Exercises 4350, write the partial fraction decomposition of the ...
 6.6.1.50: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.50: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.50: Five hundred gallons of 89octane gasoline is obtained by mixing 87...
 6.6.6.50: HOW DO YOU SEE IT? Using the constraint region shown below, determi...
 6.6.3.50: In Exercises 4954, find the equation of the parabola that passes th...
 6.50: Agriculture A mixture of 6 gallons of chemical A, 8 gallons of chem...
 6.6.4.51: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.51: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.51: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.51: Investment Portfolio A total of $24,000 is invested in two corporat...
 6.6.3.51: In Exercises 4954, find the equation of the parabola that passes th...
 6.51: Investment Analysis An inheritance of $40,000 was divided among thr...
 6.6.4.52: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.52: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.52: In Exercises 4752, use a graphing utility to graph the solution set...
 6.6.2.52: Investment Portfolio A total of $32,000 is invested in two municipa...
 6.6.3.52: In Exercises 4954, find the equation of the parabola that passes th...
 6.52: Sports The Old Course at St Andrews Links in St Andrews, Scotland, ...
 6.6.4.53: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.53: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.53: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.53: Prescriptions The numbers of prescriptions (in thousands) filled at...
 6.6.3.53: In Exercises 4954, find the equation of the parabola that passes th...
 6.53: In Exercises 53 and 54, an object moving vertically is at the given...
 6.6.4.54: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.54: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.54: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.54: Data Analysis A store manager wants to know the demand for a produc...
 6.6.3.54: In Exercises 4954, find the equation of the parabola that passes th...
 6.54: In Exercises 53 and 54, an object moving vertically is at the given...
 6.6.4.55: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.55: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.55: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.55: In Exercises 55 and 56, the sums have been evaluated. Solve the giv...
 6.6.3.55: In Exercises 5558, find the equation of the circle that passes thro...
 6.55: In Exercises 5558, write the form of the partial fraction decomposi...
 6.6.4.56: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.56: In Exercises 4956, solve the system graphically or algebraically. E...
 6.6.5.56: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.56: In Exercises 55 and 56, the sums have been evaluated. Solve the giv...
 6.6.3.56: In Exercises 5558, find the equation of the circle that passes thro...
 6.56: In Exercises 5558, write the form of the partial fraction decomposi...
 6.6.4.57: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.57: In Exercises 57 and 58, find the sales necessary to break even for ...
 6.6.5.57: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.57: Data Analysis An agricultural scientist used four test plots to det...
 6.6.3.57: In Exercises 5558, find the equation of the circle that passes thro...
 6.57: In Exercises 5558, write the form of the partial fraction decomposi...
 6.6.4.58: In Exercises 5158, write the partial fraction decomposition of the ...
 6.6.1.58: In Exercises 57 and 58, find the sales necessary to break even for ...
 6.6.5.58: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.58: Defense Department Outlays The table shows the total national outla...
 6.6.3.58: In Exercises 5558, find the equation of the circle that passes thro...
 6.58: In Exercises 5558, write the form of the partial fraction decomposi...
 6.6.4.59: The predicted cost (in thousands of dollars) for a company to remov...
 6.6.1.59: BreakEven Analysis A small software company invests $16,000 to pro...
 6.6.5.59: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.59: In Exercises 59 and 60, determine whether the statement is true or ...
 6.6.3.59: Sports In Super Bowl I, on January 15, 1967, the Green Bay Packers ...
 6.59: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.60: Thermodynamics The magnitude of the range of exhaust temperatures (...
 6.6.1.60: Choice of Two Jobs You receive two sales job offers. One company of...
 6.6.5.60: In Exercises 5360, write a system of inequalities to describe the r...
 6.6.2.60: In Exercises 59 and 60, determine whether the statement is true or ...
 6.6.3.60: Agriculture A mixture of 5 pounds of fertilizer A, 13 pounds of fer...
 6.60: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.61: In Exercises 6163, determine whether the statement is true or false...
 6.6.1.61: DVD Rentals The number of rentals of a newly released DVD of a horr...
 6.6.5.61: In Exercises 6164, (a) graph the systems representing the consumer ...
 6.6.2.61: In Exercises 61 and 62, find the value of such that the system of l...
 6.6.3.61: Finance A small corporation borrowed $775,000 to expand its clothin...
 6.61: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.62: In Exercises 6163, determine whether the statement is true or false...
 6.6.1.62: Supply and Demand The supply and demand curves for a business deali...
 6.6.5.62: In Exercises 6164, (a) graph the systems representing the consumer ...
 6.6.2.62: In Exercises 61 and 62, find the value of such that the system of l...
 6.6.3.62: Advertising A health insurance company advertises on television, on...
 6.62: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.63: In Exercises 6163, determine whether the statement is true or false...
 6.6.1.63: Log Volume Two rules for estimating the number of board feet in a l...
 6.6.5.63: In Exercises 6164, (a) graph the systems representing the consumer ...
 6.6.2.63: Writing Briefly explain whether it is possible for a consistent sys...
 6.6.3.63: In Exercises 63 and 64, find the values of and in the figure
 6.63: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.64: HOW DO YOU SEE IT? Identify the graph of the rational function and ...
 6.6.1.64: The table shows the consumption (in trillions of Btus) of geotherma...
 6.6.5.64: In Exercises 6164, (a) graph the systems representing the consumer ...
 6.6.2.64: Think About It Give examples of a system of linear equations that h...
 6.6.3.64: In Exercises 63 and 64, find the values of and in the figure
 6.64: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.65: In Exercises 6568, write the partial fraction decomposition of the ...
 6.6.1.65: In Exercises 65 and 66, find the dimensions of the rectangle meetin...
 6.6.5.65: Production A furniture company produces tables and chairs. Each tab...
 6.6.2.65: Comparing Methods Use the method of substitution to solve the syste...
 6.6.3.65: Geometry The perimeter of a triangle is 180 feet. The longest side ...
 6.65: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.66: In Exercises 6568, write the partial fraction decomposition of the ...
 6.6.1.66: In Exercises 65 and 66, find the dimensions of the rectangle meetin...
 6.6.5.66: Inventory A store sells two models of laptop computers. Because of ...
 6.6.2.66: HOW DO YOU SEE IT? Use the graphs of the two equations shown below....
 6.6.3.66: Acid Mixture A chemist needs 10 liters of a 25% acid solution. The ...
 6.66: In Exercises 5966, write the partial fraction decomposition of the ...
 6.6.4.67: In Exercises 6568, write the partial fraction decomposition of the ...
 6.6.1.67: Geometry What are the dimensions of a rectangular tract of land whe...
 6.6.5.67: Investment Analysis A person plans to invest up to $20,000 in two d...
 6.6.2.67: In Exercises 67 and 68, the graphs of the two equations appear to b...
 6.6.3.67: Electrical Network Applying Kirchhoffs Laws to the electrical netwo...
 6.67: In Exercises 6772, sketch the graph of the inequality. y 5 3y x 7 12 x
 6.6.4.68: In Exercises 6568, write the partial fraction decomposition of the ...
 6.6.1.68: Geometry What are the dimensions of a right triangle with a twoinc...
 6.6.5.68: Ticket Sales For a concert event, there are $30 reserved seat ticke...
 6.6.2.68: In Exercises 67 and 68, the graphs of the two equations appear to b...
 6.6.3.68: Pulley System A system of pulleys is loaded with 128pound and 32p...
 6.68: In Exercises 6772, sketch the graph of the inequality. 3y x 7 1
 6.6.4.69: Writing Describe two ways of solving for the constants in a partial...
 6.6.1.69: In Exercises 69 and 70, determine whether the statement is true or ...
 6.6.5.69: Truck Scheduling A small company that manufactures two models of ex...
 6.6.3.69: In Exercises 69 and 70, the sums have been evaluated. Solve the giv...
 6.69: In Exercises 6772, sketch the graph of the inequality. y 4x2 > 1
 6.6.1.70: In Exercises 69 and 70, determine whether the statement is true or ...
 6.6.5.70: A dietitian designs a special dietary supplement using two differen...
 6.6.3.70: In Exercises 69 and 70, the sums have been evaluated. Solve the giv...
 6.70: In Exercises 6772, sketch the graph of the inequality. y 3x2 2
 6.6.1.71: Think About It When solving a system of equations by substitution, ...
 6.6.5.71: Health A persons maximum heart rate is where is the persons age in ...
 6.6.3.71: Data Analysis: Stopping Distance In testing a new automobile brakin...
 6.71: In Exercises 6772, sketch the graph of the inequality. x 12 y 32 < 16y
 6.6.1.72: HOW DO YOU SEE IT? The cost of producing units and the revenue obta...
 6.6.5.72: Physical Fitness Facility An indoor running track is to be construc...
 6.6.3.72: A wildlife management team studied the reproductive rates of deer i...
 6.72: In Exercises 6772, sketch the graph of the inequality. x2 y 52 > 1x
 6.6.1.73: Think About It Consider the system of equations (a) Find values for...
 6.6.5.73: In Exercises 73 and 74, determine whether the statement is true or ...
 6.6.3.73: In Exercises 73 and 74, find values of and that satisfy the system....
 6.73: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.5.74: In Exercises 73 and 74, determine whether the statement is true or ...
 6.6.3.74: In Exercises 73 and 74, find values of and that satisfy the system....
 6.74: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.5.75: Think About It After graphing the boundary of the inequality explai...
 6.6.3.75: In Exercises 75 and 76, determine whether the statement is true or ...
 6.75: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.5.76: HOW DO YOU SEE IT? Match the system of inequalities with the graph ...
 6.6.3.76: In Exercises 75 and 76, determine whether the statement is true or ...
 6.76: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.5.77: Graphical Reasoning Two concentric circles have radii and where The...
 6.6.3.77: Think About It Are the following two systems of equations equivalen...
 6.77: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.5.78: Changing the Inequality Symbol The graph of the solution of the ine...
 6.6.3.78: HOW DO YOU SEE IT? The number of sides and the combined number of s...
 6.78: In Exercises 7378, sketch the graph (and label the vertices) of the...
 6.6.3.79: Exercises 7982, find two systems of linear equations that have the ...
 6.79: In Exercises 79 and 80, (a) graph the systems representing the cons...
 6.6.3.80: Exercises 7982, find two systems of linear equations that have the ...
 6.80: In Exercises 79 and 80, (a) graph the systems representing the cons...
 6.6.3.81: Exercises 7982, find two systems of linear equations that have the ...
 6.81: Geometry Write a system of inequalities to describe the region of a...
 6.6.3.82: Exercises 7982, find two systems of linear equations that have the ...
 6.82: Data Analysis: Sales The table shows the sales (in millions of doll...
 6.83: Inventory Costs A warehouse operator has 24,000 square feet of floo...
 6.84: Nutrition A dietitian designs a special dietary supplement using tw...
 6.85: In Exercises 8588, sketch the region determined by the constraints....
 6.86: In Exercises 8588, sketch the region determined by the constraints....
 6.87: In Exercises 8588, sketch the region determined by the constraints....
 6.88: In Exercises 8588, sketch the region determined by the constraints....
 6.89: Optimal Revenue A student is working part time as a hairdresser to ...
 6.90: Optimal Profit A manufacturer produces two models of bicycles. The ...
 6.91: In Exercises 91 and 92, determine whether the statement is true or ...
 6.92: In Exercises 91 and 92, determine whether the statement is true or ...
 6.93: In Exercises 9396, find a system of linear equations having the ord...
 6.94: In Exercises 9396, find a system of linear equations having the ord...
 6.95: In Exercises 9396, find a system of linear equations having the ord...
 6.96: In Exercises 9396, find a system of linear equations having the ord...
 6.97: In Exercises 97100, find a system of linear equations having the or...
 6.98: In Exercises 97100, find a system of linear equations having the or...
 6.99: In Exercises 97100, find a system of linear equations having the or...
 6.100: In Exercises 97100, find a system of linear equations having the or...
 6.101: Writing Explain what is meant by an inconsistent system of linear e...
 6.102: Graphical Reasoning How can you tell graphically that a system of l...
Solutions for Chapter 6: Systems of Equations and Inequalities
Full solutions for College Algebra  9th Edition
ISBN: 9781133963028
Solutions for Chapter 6: Systems of Equations and Inequalities
Get Full SolutionsChapter 6: Systems of Equations and Inequalities includes 522 full stepbystep solutions. Since 522 problems in chapter 6: Systems of Equations and Inequalities have been answered, more than 7325 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra, edition: 9. College Algebra was written by Patricia and is associated to the ISBN: 9781133963028. This expansive textbook survival guide covers the following chapters and their solutions.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.
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