 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 58830 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 and is associated to the ISBN: 9781133963028. This expansive textbook survival guide covers the following chapters and their solutions.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to 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!).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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 .

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Outer product uv T
= column times row = rank one matrix.

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.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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

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