 4.4.1.1: The pair of equations ex y 12x y 15. A is called a ______ of linear...
 4.4.3.1: The coefficients of 3x and 3x are _______ .
 4.4.5.1: ex y 2x y 41 is a system of linear ______.
 4.4.2.1: To solve the system ex y 13x 2y 8using the method discussed in this...
 4.1: Check to determine whether the ordered pair is a solution of the sy...
 4.4.4.1: Two angles are said to be ______ if the sum of their measures is 90...
 4.4.1.2: Because the ordered pair (2, 3) satisfies both equations in 1, it i...
 4.4.3.2: When the given equations are added, the variable y will be ______. ...
 4.4.5.2: To graph the linear inequality x y > 2, first graph the ______ x y ...
 4.4.2.2: We say that the equationy y = 2x + 4 is solved for ______.
 4.2: Check to determine whether the ordered pair is a solution of the sy...
 4.4.4.2: that involve moving vehicles are called uniform _______ problems. t...
 4.4.1.3: The point of ______ of the lines graphed in part (a) below is (1, 2...
 4.4.3.3: In the given system, which terms have coefficients that are opposit...
 4.4.5.3: To find the solutions of a system of two linear inequalities graphi...
 4.4.2.3: If the substitution method is used to solve e5x y 2y 3xy, which equ...
 4.3: Use the graphing method to solve each system. ex y 72x y 5e
 4.4.4.3: A length of pipe is to be cut into two pieces. The longer piece is ...
 4.4.1.4: The lines graphed in part (b) above do not intersect. They are ____...
 4.4.3.4: Fill in the blank. The objective of the elimination method is to ob...
 4.4.5.4: The phrase should not surpass can be represented by the inequality ...
 4.4.2.4: Suppose the substitution method will be used to solve ex 2y 22x 3y ...
 4.4: Use the graphing method to solve each system. 2x y 5y x3e
 4.4.4.4: Two angles are complementary. The measure of the larger angle is fo...
 4.4.1.5: A system of equations that has at least one solution is called a __...
 4.4.3.5: Add each pair of equations. a. 2a 2b 63a 2 2 b. x 3y 15x y 142a
 4.4.5.5: a. What is the equation of the boundary line of the graph of 3x y 5...
 4.4.2.5: Suppose x  4 is substituted for y in the equation x + 3y = 8. Inse...
 4.5: Use the graphing method to solve each system. e3x 6y 6x 2y 2 02x
 4.4.4.5: Two angles are supplementary. The measure of the smaller angle is 2...
 4.4.4.6: The perimeter of the following PingPong table is 28 feet. The leng...
 4.4.1.6: We call equations with different graphs ______ equations. Because _...
 4.4.3.6: a. Multiply both sides of 4x y 2 by 3. b. Multiply both sides of x ...
 4.4.5.6: a. What is the equation of the boundary line of the graph of y 4x? ...
 4.4.2.6: Fill in the blank. With the substitution method, the objective is t...
 4.6: Use the graphing method to solve each system. e6x 3y 12y 2x 2 e
 4.4.4.7: Let x = the cost of a chicken taco, in dollars, and y = the cost of...
 4.4.1.7: Refer to the illustration below. a. If the coordinates of point are...
 4.4.3.7: If the elimination method is used to solve e3x 12y 46x 4y 7x a. By ...
 4.4.5.7: Find the slope and the intercept of the line whose equation is y 4...
 4.4.2.7: A student uses the substitution method to solve the system e a 34a ...
 4.7: Find the slope and the intercept of the graph of each line in the ...
 4.4.4.8: a. Complete the following table. x y l w Principal Rate Time Intere...
 4.4.1.8: Refer to the illustration on the right. a. If the coordinates of po...
 4.4.3.8: Suppose the following system is solved using the elimination method...
 4.4.5.8: Complete the table to find the  and intercepts of the line whose ...
 4.4.2.8: a. Clear x5 2y3 1b of fractions. b. Write 2x y x 5y 3 Ax in the for...
 4.8: Bachelors Degrees. Estimate the point of intersection of the graphs...
 4.4.4.9: For each case on the right, write an algebraic expression that repr...
 4.4.1.9: a. To graph 5x 2y 10 S, we can use the intercept method. Complete t...
 4.4.3.9: What algebraic step should be performed to a. Clear 23 x 4y 45e of ...
 4.4.5.9: The boundary of the graph of 2x y > 4 is shown. a. Does the point m...
 4.4.2.9: Suppose 2 1 2x is obtained when a system is solved by the substitut...
 4.9: Use the substitution method to solve each system. ey 15 3x7y 3x 1515.
 4.4.4.10: Complete the table, which contains information about an airplane fl...
 4.4.1.10: What is the apparent solution of the system graphed in figure (a) b...
 4.4.3.10: a. Suppose 0 0 is obtained when a system is solved by the eliminati...
 4.4.5.10: Linear inequality 1 is graphed in red below and linear inequality 2...
 4.4.2.10: Suppose 2 2 is obtained when a system is solved by the substitution...
 4.10: Use the substitution method to solve each system. ex y5x 4y 3 e
 4.4.4.11: a. If the contents of the two test tubes are poured into a third tu...
 4.4.1.11: How many solutions does the system graphed in figure (b) above have...
 4.4.3.11: Complete the solution to solve the system. Solve: Add the equations...
 4.4.5.11: The graph of a system of two linear inequalities is shown. Determin...
 4.4.2.11: Complete the solution to solve the system. Solve: This is the secon...
 4.11: Use the substitution method to solve each system. e6x 2y 8 y x3x 2 ye
 4.4.4.12: a. Complete the table, which contains information about mixing two ...
 4.4.1.12: How many solutions does the system graphed on the right have? Give ...
 4.4.3.12: Write each equation in Ax + By = C form: 7x + y + 3 = 0 8x + 4 = y
 4.4.5.12: Use a check to determine whether each ordered pair is a solution of...
 4.4.2.12: The system ea 3b 2a 3b 81 was solved, and it was found that b 1 a a...
 4.12: Use the substitution method to solve each system. er 3s 7r 2s 5 e
 4.4.4.13: Complementary Angles. Two angles are complementary. The measure of ...
 4.4.1.13: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.13: Use the elimination method to solve each system. See Example 1. x y...
 4.4.5.13: Match each equation, inequality, or system with the graph of its so...
 4.4.2.13: Solve each system by substitution. See Example 1. ey 2xx y 6b
 4.13: Use the substitution method to solve each system. 9x 3y 5 03x y 53e
 4.4.4.14: Supplementary Angles. Two angles are supplementary. The measure of ...
 4.4.1.14: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.14: Use the elimination method to solve each system. See Example 1. x y...
 4.4.5.14: Match the system of inequalities with the correct graph. a. ex 2y 1...
 4.4.2.14: Solve each system by substitution. See Example 1. ey 3xx y 4 e
 4.14: Use the substitution method to solve each system. x2 y2 115x16 3y16...
 4.4.4.15: Supplementary Angles. The difference of the measures of two supplem...
 4.4.1.15: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.15: Use the elimination method to solve each system. See Example 1. ex ...
 4.4.5.15: Graph the solutions of each system. See Example 1. ex 2y 32x y 1
 4.4.2.15: Solve each system by substitution. See Example 1. ey 2x 62x y 6e
 4.15: When solving a system using the substitution method, suppose you ob...
 4.4.4.16: Complementary Angles. Two angles are complementary. The measure of ...
 4.4.1.16: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.16: Use the elimination method to solve each system. See Example 1. ex ...
 4.4.5.16: Graph the solutions of each system. See Example 1. 2x y 3x 2y 1 e
 4.4.2.16: Solve each system by substitution. See Example 1. e2x y 7y 3x 8 e
 4.16: Fill in the blank. With the substitution method, the objective is t...
 4.4.4.17: Write a system of two equations in two variables to solve each prob...
 4.4.1.17: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.17: Use the elimination method to solve each system. See Example 1. 4x ...
 4.4.5.17: Graph the solutions of each system. See Example 1. ex y 1x y 1e
 4.4.2.17: Solve each system by substitution. See Example 2. ex 3y 4x 5ye
 4.17: Write each equation of the system 4x 2y 7 03y 5x 6 23. in standard ...
 4.4.4.18: Write a system of two equations in two variables to solve each prob...
 4.4.1.18: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.18: Use the elimination method to solve each system. See Example 1. 9x ...
 4.4.5.18: Graph the solutions of each system. See Example 1. ex y 2x y 2 e
 4.4.2.18: Solve each system by substitution. See Example 2. ex 5y 3x 4y ex
 4.18: Fill in the blank. With the elimination method, the basic objective...
 4.4.4.19: Write a system of two equations in two variables to solve each prob...
 4.4.1.19: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.19: Use the elimination method to solve each system. See Example 1. e2s...
 4.4.5.19: Graph the solutions of each system. See Example 2. ey 2xx 2y 6
 4.4.2.19: Solve each system by substitution. See Example 2. ey 5xx 3y 28e
 4.19: Solve each system using the elimination (addition) method. e2x y 15...
 4.4.4.20: Write a system of two equations in two variables to solve each prob...
 4.4.1.20: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.20: Use the elimination method to solve each system. See Example 1. e2x...
 4.4.5.20: Graph the solutions of each system. See Example 2. ey 2xx y 4 e
 4.4.2.20: Solve each system by substitution. See Example 2. ey 2x3x 2y 1 ey
 4.20: Solve each system using the elimination (addition) method. ex 8y 7x...
 4.4.4.21: Write a system of two equations in two variables to solve each prob...
 4.4.1.21: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.21: Use the elimination method to solve each system. See Example 2. ex ...
 4.4.5.21: Graph the solutions of each system. See Example 2. y xy 13 x 1e
 4.4.2.21: Solve each system by substitution. See Example 3. er 3s 93r 2s 13e
 4.21: Solve each system using the elimination (addition) method. 5a b 23a...
 4.4.4.22: Write a system of two equations in two variables to solve each prob...
 4.4.1.22: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.22: Use the elimination method to solve each system. See Example 2. ex ...
 4.4.5.22: Graph the solutions of each system. See Example 2. e y 3xy x 1
 4.4.2.22: Solve each system by substitution. See Example 3. ex 2y 22x 3y 11 e
 4.22: Solve each system using the elimination (addition) method. e11x 3y ...
 4.4.4.23: Write a system of two equations in two variables to solve each prob...
 4.4.1.23: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.23: Use the elimination method to solve each system. See Example 2. 7x ...
 4.4.5.23: Graph the solutions of each system. See Example 3. e x 2y 3
 4.4.2.23: Solve each system by substitution. See Example 3. 4x y 152x 3y 5e
 4.23: Solve each system using the elimination (addition) method. e9x 3y 1...
 4.4.4.24: Write a system of two equations in two variables to solve each prob...
 4.4.1.24: Determine whether the ordered pair is a solution of the given syste...
 4.4.3.24: Use the elimination method to solve each system. See Example 2. e6x...
 4.4.5.24: Graph the solutions of each system. See Example 3. x 1y 2
 4.4.2.24: Solve each system by substitution. See Example 3. e4x y 52x 3y 13 e4x
 4.24: Solve each system using the elimination (addition) method. e0.02x 0...
 4.4.4.25: Write a system of two equations in two variables to solve each prob...
 4.4.1.25: Solve each system of equations by graphing. See Example 2. e2x 3y 1...
 4.4.3.25: Use the elimination method to solve each system. See Example 3. e7x...
 4.4.5.25: Graph the solutions of each system. See Example 3. e x 0y 0
 4.4.2.25: Solve each system by substitution. See Example 4. e8x 6y 42x y 2e4
 4.25: Solve each system using the elimination (addition) method. a4 b3 11...
 4.4.4.26: Write a system of two equations in two variables to solve each prob...
 4.4.1.26: Solve each system of equations by graphing. See Example 2. e5x y 55...
 4.4.3.26: Use the elimination method to solve each system. See Example 3. e5x...
 4.4.5.26: Graph the solutions of each system. See Example 3. e x 0y 0
 4.4.2.26: Solve each system by substitution. See Example 4. e5x 4y 02x y 0 e
 4.26: Solve each system using the elimination (addition) method. 14x 1 23...
 4.4.4.27: Write a system of two equations in two variables to solve each prob...
 4.4.1.27: Solve each system of equations by graphing. See Example 2. ex y 4x ...
 4.4.3.27: Use the elimination method to solve each system. See Example 3. e7x...
 4.4.5.27: Graph the solutions of each system. See Example 4. x 0y 0x y 3
 4.4.2.27: Solve each system by substitution. See Example 4. e4x 5y 23x y 11e
 4.27: For each system, determine which method, substitution or eliminatio...
 4.4.4.28: Write a system of two equations in two variables to solve each prob...
 4.4.1.28: Solve each system of equations by graphing. See Example 2. ex y 4x ...
 4.4.3.28: Use the elimination method to solve each system. See Example 3. ex ...
 4.4.5.28: Graph the solutions of each system. See Example 4. x y 6x 2y 6x 0
 4.4.2.28: Solve each system by substitution. See Example 4. e5u 3v 54u v 4 e
 4.28: For each system, determine which method, substitution or eliminatio...
 4.4.4.29: Write a system of two equations in two variables to solve each prob...
 4.4.1.29: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.29: Use the elimination method to solve each system. See Example 4. e4x...
 4.4.5.29: Graph the solutions of each system. See Example 4. x y 4y 0x 0
 4.4.2.29: Solve each system by substitution. See Example 5. x4 y4 12x 2y y 24...
 4.29: Write a system of two equations in two variables to solve each prob...
 4.4.4.30: Write a system of two equations in two variables to solve each prob...
 4.4.1.30: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.30: Use the elimination method to solve each system. See Example 4. e3x...
 4.4.5.30: Graph the solutions of each system. See Example 4. 2x y 2y xx 0
 4.4.2.30: Solve each system by substitution. See Example 5. 5a 2b 15 5a ba3 2...
 4.30: Write a system of two equations in two variables to solve each prob...
 4.4.4.31: Write a system of two equations in two variables to solve each prob...
 4.4.1.31: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.31: Use the elimination method to solve each system. See Example 4. e5a...
 4.4.5.31: Graph the solutions of each system. e2x 3y 0y x 1
 4.4.2.31: Solve each system by substitution. See Example 5. x 5y 20 4x yy3 x2...
 4.31: Write a system of two equations in two variables to solve each prob...
 4.4.4.32: Write a system of two equations in two variables to solve each prob...
 4.4.1.32: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.32: Use the elimination method to solve each system. See Example 4. e7a...
 4.4.5.32: Graph the solutions of each system. ey 2x 4y x 1 e
 4.4.2.32: Solve each system by substitution. See Example 5. x 6y 9 5x 2yx2 34...
 4.32: Write a system of two equations in two variables to solve each prob...
 4.33: Write a system of two equations in two variables to solve each prob...
 4.4.4.33: Write a system of two equations in two variables to solve each prob...
 4.4.1.33: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.33: Use the elimination method to solve each system. See Example 5. 8x ...
 4.4.5.33: Graph the solutions of each system. ex y 2x y 1e
 4.4.2.33: Solve each system by substitution. See Example 6. e2a 4b 24a 20 2b
 4.34: Write a system of two equations in two variables to solve each prob...
 4.4.4.34: Write a system of two equations in two variables to solve each prob...
 4.4.1.34: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.34: Use the elimination method to solve each system. See Example 5. 18 ...
 4.4.5.34: Graph the solutions of each system. ey x 2y x 4 e
 4.4.2.34: Solve each system by substitution. See Example 6. e8y 15 4xx 2y 4 e
 4.35: Write a system of two equations in two variables to solve each prob...
 4.4.4.35: Write a system of two equations in two variables to solve each prob...
 4.4.1.35: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.35: Use the elimination method to solve each system. See Example 5. 34x...
 4.4.5.35: Graph the solutions of each system. 3x 4y 72x 3y 1e
 4.4.2.35: Solve each system by substitution. See Example 6. e6 y 4x2y 8x 20e8
 4.36: Write a system of two equations in two variables to solve each prob...
 4.4.4.36: Write a system of two equations in two variables to solve each prob...
 4.4.1.36: Solve each system by graphing. If a system has no solution or infin...
 4.4.3.36: Use the elimination method to solve each system. See Example 5. 13 ...
 4.4.5.36: Graph the solutions of each system. e3x y 14x y 8 e
 4.4.2.36: Solve each system by substitution. See Example 6. e2x y x y2x 4y 6 e6
 4.37: Write a system of two equations in two variables to solve each prob...
 4.4.4.37: Write a system of two equations in two variables to solve each prob...
 4.4.1.37: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.37: Use the elimination method to solve each system. If there is no sol...
 4.4.5.37: Graph the solutions of each system. e 2x y 7y 2 2x
 4.4.2.37: Solve each system by substitution. See Example 7. ey 3x 521x 7y 35e
 4.38: Write a system of two equations in two variables to solve each prob...
 4.4.4.38: Write a system of two equations in two variables to solve each prob...
 4.4.1.38: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.38: Use the elimination method to solve each system. If there is no sol...
 4.4.5.38: Graph the solutions of each system. e 2x y 6y 2(2x 3) e
 4.4.2.38: Solve each system by substitution. See Example 7. e3a 6b 15a 2b 5 ey
 4.39: Solve each system of inequalities. e5x 3y 153x y 3
 4.4.4.39: Write a system of two equations in two variables to solve each prob...
 4.4.1.39: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.39: Use the elimination method to solve each system. If there is no sol...
 4.4.5.39: Graph the solutions of each system. e2(x 2y) 63x y 5
 4.4.2.39: Solve each system by substitution. See Example 7. ex 3y 62x 4y 6 x ye
 4.40: Solve each system of inequalities. e3y xy 3x
 4.4.4.40: Write a system of two equations in two variables to solve each prob...
 4.4.1.40: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.40: Use the elimination method to solve each system. If there is no sol...
 4.4.5.40: Graph the solutions of each system. e2x 3y 02x 3y 12 e
 4.4.2.40: Solve each system by substitution. See Example 7. e9x 3y 124 3x y e
 4.41: Solve each system of inequalities. e x 0y 0
 4.4.4.41: Write a system of two equations in two variables to solve each prob...
 4.4.1.41: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.41: Use elimination to solve each system. If there is no solution, or i...
 4.4.5.41: Graph the solutions of each system. e3x y 4 03y 2x 10
 4.4.2.41: Solve each system by substitution. If a system has no solution or i...
 4.42: Solve each system of inequalities. y xy 13x 1x 3
 4.4.4.42: Write a system of two equations in two variables to solve each prob...
 4.4.1.42: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.42: Use elimination to solve each system. If there is no solution, or i...
 4.4.5.42: Graph the solutions of each system. e3x 2y 12 0x 2 y e
 4.4.2.42: Solve each system by substitution. If a system has no solution or i...
 4.43: Use a check to determine whether each ordered pair is a solution of...
 4.4.4.43: Write a system of two equations in two variables to solve each prob...
 4.4.1.43: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.43: Use elimination to solve each system. If there is no solution, or i...
 4.4.5.43: Graph the solutions of each system. x 1y xx y 3
 4.4.2.43: Solve each system by substitution. If a system has no solution or i...
 4.44: Gift Shopping. A grandmother wants to spend at least $40 but no mor...
 4.4.4.44: Write a system of two equations in two variables to solve each prob...
 4.4.1.44: Find the slope and the intercept of the graph of each line in the ...
 4.4.3.44: Use elimination to solve each system. If there is no solution, or i...
 4.4.5.44: Graph the solutions of each system. y 2.52x y 2x 2
 4.4.2.44: Solve each system by substitution. If a system has no solution or i...
 4.4.4.45: Write a system of two equations in two variables to solve each prob...
 4.4.1.45: Use a graphing calculator to solve each system. See Objective 5. ey...
 4.4.3.45: Solve the system by either the substitution or the elimination meth...
 4.4.5.45: Graph the solutions of each system. e x y 0y x 2
 4.4.2.45: Solve each system by substitution. If a system has no solution or i...
 4.4.4.46: Write a system of two equations in two variables to solve each prob...
 4.4.1.46: Use a graphing calculator to solve each system. See Objective 5. e3...
 4.4.3.46: Solve the system by either the substitution or the elimination meth...
 4.4.5.46: Graph the solutions of each system. y 2x 0y 12 x 2 e
 4.4.2.46: Solve each system by substitution. If a system has no solution or i...
 4.4.4.47: Write a system of two equations in two variables to solve each prob...
 4.4.1.47: Use a graphing calculator to solve each system. See Objective 5. e6...
 4.4.3.47: Solve the system by either the substitution or the elimination meth...
 4.4.5.47: In part a, graph the solution of each system. Use your answer to pa...
 4.4.2.47: Solve each system by substitution. If a system has no solution or i...
 4.4.4.48: Write a system of two equations in two variables to solve each prob...
 4.4.1.48: Use a graphing calculator to solve each system. See Objective 5. ex...
 4.4.3.48: Solve the system by either the substitution or the elimination meth...
 4.4.5.48: In part a, graph the solution of each system. Use your answer to pa...
 4.4.2.48: Solve each system by substitution. If a system has no solution or i...
 4.4.4.49: Write a system of two equations in two variables to solve each prob...
 4.4.1.49: Solve each system of equations by graphing. ey 3x 6y 2x 4e
 4.4.3.49: Solve the system by either the substitution or the elimination meth...
 4.4.5.49: Birds of Prey. Parts (a) and (b) of the illustration show the field...
 4.4.2.49: Solve each system by substitution. If a system has no solution or i...
 4.4.4.50: Write a system of two equations in two variables to solve each prob...
 4.4.1.50: Solve each system of equations by graphing. ey x 3y 2x 3 ey
 4.4.3.50: Solve the system by either the substitution or the elimination meth...
 4.4.5.50: Earth Science. Shade the area of the earths surface that is north o...
 4.4.2.50: Solve each system by substitution. If a system has no solution or i...
 4.4.4.51: Write a system of two equations in two variables to solve each prob...
 4.4.1.51: Solve each system of equations by graphing. e2y 3x 23x 2y 6e
 4.4.3.51: Solve the system by either the substitution or the elimination meth...
 4.4.5.51: In 5154, graph each system of inequalities and give two possible so...
 4.4.2.51: Solve each system by substitution. If a system has no solution or i...
 4.4.4.52: Write a system of two equations in two variables to solve each prob...
 4.4.1.52: Solve each system of equations by graphing. e3x 6y 18x 2y 3 e
 4.4.3.52: Solve the system by either the substitution or the elimination meth...
 4.4.5.52: In 5154, graph each system of inequalities and give two possible so...
 4.4.2.52: Solve each system by substitution. If a system has no solution or i...
 4.4.4.53: Explain why a table is helpful in solving uniform motion and mixtur...
 4.4.1.53: Solve each system of equations by graphing. ex y 2y x 4e
 4.4.3.53: Solve the system by either the substitution or the elimination meth...
 4.4.5.53: In 5154, graph each system of inequalities and give two possible so...
 4.4.2.53: Solve each system by substitution. If a system has no solution or i...
 4.4.2.54: Solve each system by substitution. If a system has no solution or i...
 4.4.4.54: A man paid $89 for two shirts and four pairs of socks. If we let th...
 4.4.1.54: Solve each system of equations by graphing. ex y 1y x 5 e
 4.4.3.54: Solve the system by either the substitution or the elimination meth...
 4.4.5.54: In 5154, graph each system of inequalities and give two possible so...
 4.4.2.55: Solve each system by substitution. If a system has no solution or i...
 4.4.4.55: Graph each inequality. Then describe the graph using interval notat...
 4.4.1.55: Solve each system of equations by graphing. ex 33y 6 2xe
 4.4.3.55: Solve the system by either the substitution or the elimination meth...
 4.4.5.55: Photographer In some cameras, the image that you see in the viewfin...
 4.4.2.56: Solve each system by substitution. If a system has no solution or i...
 4.4.4.56: Graph each inequality. Then describe the graph using interval notat...
 4.4.1.56: Solve each system of equations by graphing. ex 42y 12 4x e
 4.4.3.56: Solve the system by either the substitution or the elimination meth...
 4.4.5.56: Pesticides. To get rid of fruit flies, helicopters sprayed an area ...
 4.4.2.57: Solve each system by substitution. If a system has no solution or i...
 4.4.4.57: Graph each inequality. Then describe the graph using interval notat...
 4.4.1.57: Solve each system of equations by graphing. y 34x 3y x4 175.
 4.4.3.57: Solve the system by either the substitution or the elimination meth...
 4.4.5.57: Explain the error. Graph: y xx y 1yy x + y = 1 y = x 111 1 2 3 4 2 ...
 4.4.2.58: Solve each system by substitution. If a system has no solution or i...
 4.4.4.58: Graph each inequality. Then describe the graph using interval notat...
 4.4.1.58: Solve each system of equations by graphing. y 23x 4y x3 7
 4.4.3.58: Solve the system by either the substitution or the elimination meth...
 4.4.5.58: When a solution of a system of linear inequalities is graphed, what...
 4.4.2.59: Solve each system by substitution. If a system has no solution or i...
 4.4.4.59: Three types of hardware items, nails, bolts, and nuts, are placed o...
 4.4.1.59: Solve each system of equations by graphing. ey x 2y 3x 6y
 4.4.3.59: Solve the system by either the substitution or the elimination meth...
 4.4.5.59: Describe how the graphs of the solutions of these systems are simil...
 4.4.2.60: Solve each system by substitution. If a system has no solution or i...
 4.4.4.60: Farming. In a pen of goats and chickens, there are 40 heads and 130...
 4.4.1.60: Solve each system of equations by graphing. ey 2x 4y 5x 3 ey
 4.4.3.60: Solve the system by either the substitution or the elimination meth...
 4.4.5.60: Explain when a system of inequalities will have no solutions.
 4.4.2.61: Solve each system by substitution. If a system has no solution or i...
 4.4.1.61: Solve each system of equations by graphing. ex 3y 113x y 17ey
 4.4.3.61: Solve the system by either the substitution or the elimination meth...
 4.4.5.61: Simplify each expression. 81 34 t2
 4.4.2.62: Solve each system by substitution. If a system has no solution or i...
 4.4.1.62: Solve each system of equations by graphing. e2x 3y 183x 2y 1 ex
 4.4.3.62: Solve the system by either the substitution or the elimination meth...
 4.4.5.62: Simplify each expression. 231 (3w 6)
 4.4.2.63: Solve each system by substitution. If a system has no solution or i...
 4.4.1.63: Solve each system of equations by graphing. ex y 2y xe
 4.4.3.63: Solve the system by either the substitution or the elimination meth...
 4.4.5.63: Simplify each expression. 716 x 316 x
 4.4.2.64: Solve each system by substitution. If a system has no solution or i...
 4.4.1.64: Solve each system of equations by graphing. ex y 4y x e
 4.4.3.64: Solve the system by either the substitution or the elimination meth...
 4.4.5.64: Simplify each expression. 60a 320 r 415 b 7
 4.4.2.65: Solve each system by substitution. If a system has no solution or i...
 4.4.1.65: Solve each system of equations by graphing. e4x 2y 8y 2x 4e
 4.4.3.65: Solve the system by either the substitution or the elimination meth...
 4.4.5.65: Graph the solutions of each system. x3 y2 3x3 y2 16
 4.4.2.66: Solve each system by substitution. If a system has no solution or i...
 4.4.1.66: Solve each system of equations by graphing. e2y 6x 123x y 6 e4x
 4.4.3.66: Solve the system by either the substitution or the elimination meth...
 4.4.5.66: Graph the solutions of each system. e 3x y 2y 3(1 x)
 4.4.2.67: Solve each system by substitution. If a system has no solution or i...
 4.4.1.67: Solve each system of equations by graphing. ex 4y 2y x 5e2
 4.4.3.67: Solve the system by either the substitution or the elimination meth...
 4.4.5.67: Graph the solutions of each system. 2x 3y 63x y 1x 0e
 4.4.2.68: Solve each system by substitution. If a system has no solution or i...
 4.4.1.68: Solve each system of equations by graphing. e3x 2y 82x 3y 1 ex
 4.4.3.68: Solve the system by either the substitution or the elimination meth...
 4.4.5.68: Graph the solutions of each system. x 0y 09x 3y 183x 6y 18
 4.4.2.69: Solve each system by substitution. If a system has no solution or i...
 4.4.1.69: Solve each system of equations by graphing. ey 3x 2y 4e3
 4.4.3.69: Solve the system by either the substitution or the elimination meth...
 4.4.2.70: Solve each system by substitution. If a system has no solution or i...
 4.4.1.70: Solve each system of equations by graphing. ey 42x y 8 ey
 4.4.3.70: Solve the system by either the substitution or the elimination meth...
 4.4.2.71: Solve each system by substitution. If a system has no solution or i...
 4.4.1.71: Solve each system of equations by graphing. 2y 4x 12y 6e
 4.4.3.71: Solve the system by either the substitution or the elimination meth...
 4.4.2.72: Solve each system by substitution. If a system has no solution or i...
 4.4.1.72: Solve each system of equations by graphing. 23x y 33x y 3x
 4.4.3.72: Solve the system by either the substitution or the elimination meth...
 4.4.2.73: Solve each system by substitution. If a system has no solution or i...
 4.4.1.73: Social Networks. Refer to the graph below. In what month did Facebo...
 4.4.3.73: Solve the system by either the substitution or the elimination meth...
 4.4.2.74: Solve each system by substitution. If a system has no solution or i...
 4.4.1.74: Beverages. Refer to the graph below. In what year was average numbe...
 4.4.3.74: Solve the system by either the substitution or the elimination meth...
 4.4.2.75: Solve each system by substitution. If a system has no solution or i...
 4.4.1.75: Latitude and Longitude. Refer to the following map.a. Name three Am...
 4.4.3.75: Solve the system by either the substitution or the elimination meth...
 4.4.2.76: Solve each system by substitution. If a system has no solution or i...
 4.4.1.76: Economics. The following graph illustrates the law of supply and de...
 4.4.3.76: Solve the system by either the substitution or the elimination meth...
 4.4.2.77: Solve each system by substitution. If a system has no solution or i...
 4.4.1.77: Daily Tracking Polls. Refer to the graph below.a. Which political c...
 4.4.3.77: Solve the system by either the substitution or the elimination meth...
 4.4.2.78: Solve each system by substitution. If a system has no solution or i...
 4.4.1.78: Air Traffic Control. The equations describing the paths of two airp...
 4.4.3.78: Solve the system by either the substitution or the elimination meth...
 4.4.2.79: Solve each system by substitution. If a system has no solution or i...
 4.4.1.79: Photographer Photographers often use the rule of thirds to add more...
 4.4.3.79: Solve the system by either the substitution or the elimination meth...
 4.4.2.80: Solve each system by substitution. If a system has no solution or i...
 4.4.1.80: TV Coverage. A television camera is located at (2, 0) and will foll...
 4.4.3.80: Solve the system by either the substitution or the elimination meth...
 4.4.2.81: Solve each system by substitution. If a system has no solution or i...
 4.4.1.81: Explain why it is difficult to determine the solution of the system...
 4.4.3.81: Solve the system by either the substitution or the elimination meth...
 4.4.2.82: Solve each system by substitution. If a system has no solution or i...
 4.4.1.82: Without graphing, how can you tell that the graphs of y = 2x + 1 an...
 4.4.3.82: Solve the system by either the substitution or the elimination meth...
 4.4.2.83: Offroading. The angle of approach indicates how steep of an incline...
 4.4.1.83: Could a system of two linear equations have exactly two solutions? ...
 4.4.3.83: Solve the system by either the substitution or the elimination meth...
 4.4.2.84: High School Sports. The equations shown in the following graph mode...
 4.4.1.84: What is an inconsistent system? What are dependent equations?
 4.4.3.84: Solve the system by either the substitution or the elimination meth...
 4.4.2.85: Geometry. In the illustration, x and y represent the degree measure...
 4.4.1.85: Suppose the graphs of the two linear equations of a system are the ...
 4.4.3.85: Solve the system by either the substitution or the elimination meth...
 4.4.2.86: Geometry. In the illustration, x and y represent the degree measure...
 4.4.1.86: The Swine Flu. The graph below is for the month of January, 2010. I...
 4.4.3.86: Solve the system by either the substitution or the elimination meth...
 4.4.2.87: What concept does this diagram illustrate? e6x 5y 11y 3x 267
 4.4.1.87: Solve each inequality. Write the solution set in interval notation ...
 4.4.3.87: Solve the system by either the substitution or the elimination meth...
 4.4.2.88: Explain the error. Solve: Solve for a in the second equation. Subst...
 4.4.1.88: Solve each inequality. Write the solution set in interval notation ...
 4.4.3.88: Solve the system by either the substitution or the elimination meth...
 4.4.2.89: When using the substitution method, how can you tell whether a. a s...
 4.4.1.89: Solve each inequality. Write the solution set in interval notation ...
 4.4.3.89: Solve the system by either the substitution or the elimination meth...
 4.4.2.90: When solving a system, what advantages are there with the substitut...
 4.4.1.90: Solve each inequality. Write the solution set in interval notation ...
 4.4.3.90: Solve the system by either the substitution or the elimination meth...
 4.4.2.91: Consider the equation 5x + y = 12. Explain why it is easier to solv...
 4.4.1.91: Can a system of two linear equations in two variables be inconsiste...
 4.4.3.91: Education. The graph shows educational trends during the years 1980...
 4.4.2.92: Could the substitution method be used to solve the following system...
 4.4.1.92: Construct a system of two linear equations that has a solution of (...
 4.4.3.92: Newspapers. The graph shows the trends in the newspaper publishing ...
 4.4.2.93: Find the prime factorization of 189.
 4.4.1.93: Write a system of two linear equations such that (2, 3) is a soluti...
 4.4.3.93: CFL Bulbs. The graph below shows how a more expensive, but more ene...
 4.4.2.94: Complete each statement. For any nonzero number a. a. 0aa b. a0is
 4.4.1.94: Solve by graphing: 3 x 12y 162x5 y2 1310(2
 4.4.3.94: The Human Skeleton. The equation h f 53 models the fact that the nu...
 4.4.2.95: Add: 51214
 4.4.3.95: Why is the method for solving systems that is discussed in this sec...
 4.4.2.96: Divide: 13 45
 4.4.3.96: If the elimination method is to be used to solve this system, what ...
 4.4.2.97: Use the substitution method to solve each system. 6x 13 53 3y 121 5...
 4.4.3.97: Can the system e2x 3y 137x 3y 5100 be solved more easily using the ...
 4.4.2.98: Use the substitution method to solve each system. e0.5x 0.5y 60.001...
 4.4.3.98: Explain the error in the following work. Solve: ex y 1x y 5e x y 1x...
 4.4.2.99: Use the substitution method to solve each system. e2(2x 3y) 58x 3(1...
 4.4.3.99: Find an equation of the line with slope 116that passes through (2, ...
 4.4.2.100: The system has infinitely many solutions. Find three of them.12x y ...
 4.4.3.100: Solve S 2prh 2pr2 for h
 4.4.3.101: Evaluate: 10(18 42)3S
 4.4.3.102: Evaluate: 52
 4.4.3.103: Use the elimination method to solve each system. x 32 116 y 53x 33 ...
 4.4.3.104: Use the elimination method to solve each system. 4(x 1)34 12 3(y 1)...
Solutions for Chapter 4: Systems of Linear Equations and Inequalities
Full solutions for Elementary and Intermediate Algebra  5th Edition
ISBN: 9781111567682
Solutions for Chapter 4: Systems of Linear Equations and Inequalities
Get Full SolutionsElementary and Intermediate Algebra was written by and is associated to the ISBN: 9781111567682. Since 470 problems in chapter 4: Systems of Linear Equations and Inequalities have been answered, more than 37814 students have viewed full stepbystep solutions from this chapter. Chapter 4: Systems of Linear Equations and Inequalities includes 470 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Elementary and Intermediate Algebra, edition: 5.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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)ยท(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 .

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).