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Study Guide and Review - Chapter 6 State whether each sentence is true or false. If false, replace the underlined term to make a true sentence. 1. If a system has at least one solution, it is said to be consistent. SOLUTION: If a system has at least one solution, it is said to be consistent. So, the statement is true. 2. If a consistent system has exactly two solution(s), it is said to be independent. SOLUTION: The statement is false. If a consistent system has exactly one solution(s), it is said to be independent. 3. If a consistent system has an infinite number of solutions, it is said to be inconsistent. SOLUTION: The statement is false. If a consistent system has an infinite number of solutions, it is said to be dependent. 4. If a system has no solution, it is said to be inconsistent. SOLUTION: If a system has no solution, it is said to be inconsistent. So, the statement is true. 5. Substitution involves substituting an expression from one equation for a variable in the other. SOLUTION: Substitution involves substituting an expression from one equation for a variable in the other. So, the statement is true. 6. In some cases, dividing two equations in a system together will eliminate one of the variables. This process is called elimination. SOLUTION: The statement is false. In some cases, when adding or subtracting two equations in a system together will eliminate one of the variables, this process is called elimination. 7. A set of two or more inequalities with the same variables is called a system of equations. SOLUTION: The statement is false. A set of two or more inequalities with the same variables is called a system of inequalities. 8. When the graphs of the inequalities in a system of inequalities do not intersect, there are no solutions to the system. SOLUTION: True Graph each system and determine the number of solutions that it has. If it has one solution, name it. 9. x − y = 1 x +y = 5 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: eSolutions Manual - Powered by Cognero Page 1 The statement is false. A set of two or more inequalities with the same variables is called a system of inequalities. 8. When the graphs of the inequalities in a system of inequalities do not intersect, there are no solutions to the system. SOLUTION: Study Guide and Review - Chapter 6 True Graph each system and determine the number of solutions that it has. If it has one solution, name it. 9. x − y = 1 x +y = 5 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: Equation 2: Graph and locate the solution. y=x−1 y = −x + 5 The graphs appear to intersect at the point (3, 2). You can check this by substituting 3 for x and 2 for y. The solution is (3, 2). 10. y = 2x − 4 4x + y = 2 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 2: eSolutions Manual - Powered by Cognero Page 2 Study Guide andisReview The solution (3, 2). - Chapter 6 10. y = 2x − 4 4x + y = 2 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 2: Graph and find the solution. y = 2x − 4 y = −4x + 2 The graphs appear to intersect at the point (1, −2). You can check this by substituting 1 for x and −2 for y. The solution is (1, −2). 11. 2x − 3y = −6 y = −3x + 2 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: eSolutions Manual - Powered by Cognero Page 3 Guide and Review - Chapter 6 Study The solution is (1, −2). 11. 2x − 3y = −6 y = −3x + 2 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: Graph and find the solution. y= x+2 y = −3x + 2 The graphs appear to intersect at the point (0, 2). You can check this by substituting 0 for x and 2 for y. The solution is (0, 2). 12. −3x + y = −3 y =x−3 SOLUTION: To graph the system, write both equations in slope-intercept form. Manual - Powered by Cognero eSolutions Equation 1: Page 4 Guide and Review - Chapter 6 Study The solution is (0, 2). 12. −3x + y = −3 y =x−3 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: Graph and find the solution. y = 3x − 3 y=x−3 The graphs appear to intersect at the point (0, −3). You can check this by substituting 0 for x and −3 for y. The solution is (0, −3). 13. x + 2y = 6 3x + 6y = 8 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: eSolutions Manual - Powered by Cognero Page 5 Guide and Review - Chapter 6 Study The solution is (0, −3). 13. x + 2y = 6 3x + 6y = 8 SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: Equation 2: Graph each equation. y= x+3 y= x+ The lines have the same slope but different y-intercepts, so the lines are parallel. Since they do not intersect, there is no solution of this system. The system is inconsistent. eSolutions 14. 3x +Manual y = 5 - Powered by Cognero 6x = 10 − 2y Page 6 Study Guide The lines and haveReview the same- Chapter slope but 6different y-intercepts, so the lines are parallel. Since they do not intersect, there is no solution of this system. The system is inconsistent. 14. 3x + y = 5 6x = 10 − 2y SOLUTION: To graph the system, write both equations in slope-intercept form. Equation 1: Equation 2: Graph the equations. y = −3x + 5 y = −3x + 5 The two lines are identical, so there are an infinite number of solutions to the system. The system is dependent. 15. MAGIC NUMBERS Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two variables, write a system of equations, and solve by graphing. SOLUTION: Sample answer: Let x be one number and y be the other number. x + y = 14 x − yManual = 4 - Powered by Cognero eSolutions To graph the system, write both equations in slope-intercept form. Page 7 Guide and Review - Chapter 6 Study The two lines are identical, so there are an infinite number of solutions to the system. The system is dependent. 15. MAGIC NUMBERS Sean is trying to find two numbers with a sum of 14 and a difference of 4. Define two variables, write a system of equations, and solve by graphing. SOLUTION: Sample answer: Let x be one number and y be the other number. x + y = 14 x −y = 4 To graph the system, write both equations in slope-intercept form. Equation 1: Equation 2: Graph the equations and find the solution. y = −x + 14 y=x−4 The graphs appear to intersect at the point (9, 5). So, the numbers 9 and 5 have a sum of 14 and a difference of 4. Use substitution to solve each system of equations. 16. x + y = 3 x = 2y eSolutions Manual - Powered by Cognero SOLUTION: x +y = 3 Page 8 Guide and Review - Chapter 6 Study The graphs appear to intersect at the point (9, 5). So, the numbers 9 and 5 have a sum of 14 and a difference of 4. Use substitution to solve each system of equations. 16. x + y = 3 x = 2y SOLUTION: x +y = 3 x = 2y Substitute 2y for x in the first equation. Use the solution for y and either equation to find x. x = 2y x = 2(1) x =2 The solution is (2, 1). 17. x + 3y = −28 y = −5x SOLUTION: x + 3y = −28 y = −5x Substitute −5x for y in the first equation. Use the solution for x and either equation to find y. The solution is (2, −10). 18. 3x + 2y = 16 x = 3y − 2 SOLUTION: 3x +Manual 2y = 16 eSolutions - Powered by Cognero x = 3y − 2 Page 9 Guide and Review - Chapter 6 Study The solution is (2, −10). 18. 3x + 2y = 16 x = 3y − 2 SOLUTION: 3x + 2y = 16 x = 3y − 2 Substitute 3y − 2 for x in the first equation. Use the solution for y and either equation to find x. The solution is (4, 2). 19. x − y = 8 y = −3x SOLUTION: x −y = 8 y = −3x Substitute −3x for y in the first equation. Use the solution for x and either equation to find y. The solution is (2, −6). eSolutions Manual - Powered by Cognero 20. y = 5x − 3 x + 2y = 27 Page 10 Guide and Review - Chapter 6 Study The solution is (4, 2). 19. x − y = 8 y = −3x SOLUTION: x −y = 8 y = −3x Substitute −3x for y in the first equation. Use the solution for x and either equation to find y. The solution is (2, −6). 20. y = 5x − 3 x + 2y = 27 SOLUTION: y = 5x − 3 x + 2y = 27 Substitute 5x − 3 for y in the second equation. Use the solution for x and either equation to find y. The solution is (3, 12). 21. x + 3y = 9 - Powered by Cognero eSolutions Manual x +y = 1 SOLUTION: Page 11 Study Guide and Review - Chapter 6 The solution is (3, 12). 21. x + 3y = 9 x +y = 1 SOLUTION: x + 3y = 9 x +y = 1 First, solve the second equation for y to get y = −x +1. Then substitute −x + 1 for y in the first equation. Use the solution for x and either equation to find y. The solution is (−3, 4). 22. GEOMETRY The perimeter of a rectangle is 48 inches. The length is 6 inches greater than the width. Define the variables, and write equations to represent this situation. Solve the system by using substitution. SOLUTION: Sample answer: Let w be the width and be the length. 2 + 2w = 48 =w+6 Substitute w + 6 for in the first equation. Use the solution for w and either equation to find . =w+6 =9+6 = 15 The solution is (9, 15). Use Manual elimination each eSolutions - Poweredto bysolve Cognero 23. x + y = 13 x −y = 5 system of equations. Page 12 =w+6 =9+6 = 15 Study Guide and Review - Chapter 6 The solution is (9, 15). Use elimination to solve each system of equations. 23. x + y = 13 x −y = 5 SOLUTION: Because y and −y have opposite coefficients, add the equations. Now, substitute 9 for x in either equation to find y. The solution is (9, 4). 24. −3x + 4y = 21 3x + 3y = 14 SOLUTION: Because −3x and 3x have opposite coefficients, add the equations. Now, substitute 5 for y in either equation to find x. The solution is . 25. x + 4y = −4 x + 10y = −16 SOLUTION: eSolutions Manual - Powered by Cognero Page 13 Because x and x have the same coefficients, multiply equation 1 by –1 so the x's are additive inverses. Then add the equations. Study Guide andisReview - .Chapter 6 The solution 25. x + 4y = −4 x + 10y = −16 SOLUTION: Because x and x have the same coefficients, multiply equation 1 by –1 so the x's are additive inverses. Then add the equations. Now, substitute −2 for y in either equation to find x. The solution is (4, −2). 26. 2x + y = −5 x −y = 2 SOLUTION: Because y and −y have opposite coefficients, add the equations. Now, substitute −1 for x in either equation to find y. The solution is (−1, −3). 27. 6x + y = 9 −6x + 3y = 15 eSolutions Manual - Powered by Cognero SOLUTION: Page 14 Guide and Review - Chapter 6 Study The solution is (−1, −3). 27. 6x + y = 9 −6x + 3y = 15 SOLUTION: Because 6x and −6x have opposite coefficients, add the equations. Now, substitute 6 for y in either equation to find x. The solution is . 28. x − 4y = 2 3x + 4y = 38 SOLUTION: Because −4y and 4y have opposite coefficients, add the equations. Now, substitute 10 for x in either equation to find y. The solution is (10, 2). 29. 2x + 2y = 4 2x − 8y = −46 SOLUTION: Because 2x and 2x have the same coefficients, you need to multiply equation 2 by -1 so they are additive inverses. Then add the equations. eSolutions Manual - Powered by Cognero Page 15 Study Guide and Review - Chapter 6 The solution is (10, 2). 29. 2x + 2y = 4 2x − 8y = −46 SOLUTION: Because 2x and 2x have the same coefficients, you need to multiply equation 2 by -1 so they are additive inverses. Then add the equations. Now, substitute 5 for y in either equation to find x. The solution is (−3, 5). 30. 3x + 2y = 8 x + 2y = 2 SOLUTION: Because 2y and 2y have same coefficients, multiply equation 2 by –1 so the terms are additive inverses. Then add the equations. Now, substitute 3 for x in either equation to find y. eSolutions Manual - Powered by Cognero Page 16 Study Guide and Review - Chapter 6 The solution is (−3, 5). 30. 3x + 2y = 8 x + 2y = 2 SOLUTION: Because 2y and 2y have same coefficients, multiply equation 2 by –1 so the terms are additive inverses. Then add the equations. Now, substitute 3 for x in either equation to find y. The solution is . 31. BASEBALL CARDS Cristiano bought 24 baseball cards for $50. One type cost $1 per card, and the other cost $3 per card. Define the variables, and write equations to find the number of each type of card he bought. Solve by using elimination. SOLUTION: Sample answer: Let f be the first type of card and let c be the second type of card. f + c = 24 (total number of cards) f + 3c = 50 (cost of the cards) Because f and f have the same coefficients, multiply equation 2 by –1 and then add the equations. eSolutions Manual - Powered by Cognero Now, substitute 13 for c in either equation to find f . Page 17 Study Guide andisReview - .Chapter 6 The solution 31. BASEBALL CARDS Cristiano bought 24 baseball cards for $50. One type cost $1 per card, and the other cost $3 per card. Define the variables, and write equations to find the number of each type of card he bought. Solve by using elimination. SOLUTION: Sample answer: Let f be the first type of card and let c be the second type of card. f + c = 24 (total number of cards) f + 3c = 50 (cost of the cards) Because f and f have the same coefficients, multiply equation 2 by –1 and then add the equations. Now, substitute 13 for c in either equation to find f . The solution is (11, 13). Cristiano bought 11 $1 cards and 13 $3 cards. Use elimination to solve each system of equations. 32. x + y = 4 −2x + 3y = 7 SOLUTION: Notice that if you multiply the first equation by 2, the coefficients of the x-terms are additive inverses. Now, substitute 3 for y in either equation to find x. The solution is (1, 3). eSolutions Manual - Powered by Cognero 33. x − y = −2 2x + 4y = 38 Page 18 Study Guide andisReview The solution (11, 13).- Chapter 6 Cristiano bought 11 $1 cards and 13 $3 cards. Use elimination to solve each system of equations. 32. x + y = 4 −2x + 3y = 7 SOLUTION: Notice that if you multiply the first equation by 2, the coefficients of the x-terms are additive inverses. Now, substitute 3 for y in either equation to find x. The solution is (1, 3). 33. x − y = −2 2x + 4y = 38 SOLUTION: Notice that if you multiply the first equation by 4, the coefficients of the y-terms are additive inverses. Now, substitute 5 for x in either equation to find y. The solution is (5, 7). 34. 3x + 4y = 1 5x + 2y = 11 SOLUTION: Notice that if you multiply the second equation by −2, the coefficients of the y-terms are additive inverses. eSolutions Manual - Powered by Cognero Page 19 Study Guide and Review - Chapter 6 The solution is (5, 7). 34. 3x + 4y = 1 5x + 2y = 11 SOLUTION: Notice that if you multiply the second equation by −2, the coefficients of the y-terms are additive inverses. Now, substitute 3 for x in either equation to find y. The solution is (3, −2). 35. −9x + 3y = −3 3x − 2y = −4 SOLUTION: Notice that if you multiply the second equation by 3, the coefficients of the x-terms are additive inverses. Now, substitute 5 for y in either equation to find x. The solution is (2, 5). 36. 8x − 3y = −35 3x + 4y = 33 SOLUTION: Notice that if you multiply the first equation by 4 and the second equation by 3, the coefficients of the y-terms are additive inverses. Manual - Powered by Cognero eSolutions Page 20 Study Guide and Review - Chapter 6 The solution is (2, 5). 36. 8x − 3y = −35 3x + 4y = 33 SOLUTION: Notice that if you multiply the first equation by 4 and the second equation by 3, the coefficients of the y-terms are additive inverses. Now, substitute −1 for x in either equation to find y. The solution is (−1, 9). 37. 2x + 9y = 3 5x + 4y = 26 SOLUTION: Notice that if you multiply the first equation by 5 and the second equation by −2, the coefficients of x-terms are additive inverses. Now, substitute −1 for y in either equation to find x. The solution is (6, −1). 38. −7x + 3y = 12 2x − 8y = −32 SOLUTION: Notice that- ifPowered you multiply the first equation by 2 and the second equation by 7, the coefficients of the x-terms are eSolutions Manual by Cognero Page 21 additive inverses. Guide and Review - Chapter 6 Study The solution is (6, −1). 38. −7x + 3y = 12 2x − 8y = −32 SOLUTION: Notice that if you multiply the first equation by 2 and the second equation by 7, the coefficients of the x-terms are additive inverses. Now, substitute 4 for y in either equation to find x. The solution is (0, 4). 39. 8x − 5y = 18 6x + 6y = −6 SOLUTION: Notice that if you multiply the first equation by 6 and the second equation by 5, the coefficients of the y-terms are additive inverses. Now, substitute 1 for x in either equation to find y. The solution is (1, −2). 40. BAKE SALE On the first day, a total of 40 items were sold for $356. Define the variables, and write a system of equations to find the number of cakes and pies sold. Solve by using elimination. eSolutions Manual - Powered by Cognero Page 22 Guide and Review - Chapter 6 Study The solution is (1, −2). 40. BAKE SALE On the first day, a total of 40 items were sold for $356. Define the variables, and write a system of equations to find the number of cakes and pies sold. Solve by using elimination. SOLUTION: Let c represent the cakes and let p represent the pies. 8c + 10p = 356 c + p = 40 Notice that if you multiply the second equation by −8, the coefficients of the c-terms are additive inverses. Now, substitute 18 for p in either equation to find c. The solution is (22, 18). The Monarch Band Booster sold 22 cakes and 18 pies. Determine the best method to solve each system of equations. Then solve the system. 41. y = x − 8 y = −3x SOLUTION: Because both equations are solved for one of the variables, substitution is the best method. Substitute −3x for y in the first equation. Substitute 2 for x in either equation to find y. Manual - Powered by Cognero eSolutions Page 23 The solution (22, 18).- Chapter 6 Study Guide andisReview The Monarch Band Booster sold 22 cakes and 18 pies. Determine the best method to solve each system of equations. Then solve the system. 41. y = x − 8 y = −3x SOLUTION: Because both equations are solved for one of the variables, substitution is the best method. Substitute −3x for y in the first equation. Substitute 2 for x in either equation to find y. The solution is (2, −6). 42. y = −x y = 2x SOLUTION: Because both equations are solved for one of the variables, substitution is the best method. Substitute 2x for y in the first equation. Substitute 0 for x in either equation to find y. The solution is (0, 0). 43. x + 3y = 12 x = −6y SOLUTION: Because one of the equations is solved for one of the variables, substitution is the best method. Substitute −6y for x in the first equation. eSolutions Manual - Powered by Cognero Page 24 Study Guide and Review - Chapter 6 The solution is (0, 0). 43. x + 3y = 12 x = −6y SOLUTION: Because one of the equations is solved for one of the variables, substitution is the best method. Substitute −6y for x in the first equation. Substitute −4 for y in either equation to find x. The solution is (24, −4). 44. x + y = 10 x − y = 18 SOLUTION: Because y and −y have opposite coefficients, elimination using addition is the best method. Now, substitute 14 for x in either equation to find y. The solution is (14, −4). 45. 3x + 2y = −4 5x + 2y = −8 SOLUTION: Because 2y and 2y have the same coefficient, elimination using addition is the best method. Multiply equation 2 by – 1. eSolutions Manual - Powered by Cognero Page 25 Guide and Review - Chapter 6 Study The solution is (14, −4). 45. 3x + 2y = −4 5x + 2y = −8 SOLUTION: Because 2y and 2y have the same coefficient, elimination using addition is the best method. Multiply equation 2 by – 1. Now, substitute −2 for x in either equation to find y. The solution is (−2, 1). 46. 6x + 5y = 9 −2x + 4y = 14 SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the second equation by 3, the coefficients of the x-terms are additive inverses. Now, substitute 3 for y in either equation to find x. eSolutions - Powered The Manual solution is (−1, by 3).Cognero 47. 3x + 4y = 26 Page 26 Study Guide and Review - Chapter 6 The solution is (−2, 1). 46. 6x + 5y = 9 −2x + 4y = 14 SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the second equation by 3, the coefficients of the x-terms are additive inverses. Now, substitute 3 for y in either equation to find x. The solution is (−1, 3). 47. 3x + 4y = 26 2x + 3y = 19 SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the first equation by 2 and the second equation by −3, the coefficients of the x-terms are additive inverses. Now, substitute 5 for y in either equation to find x. The solution is (2, 5). 48. 11x − 6y = 3 5x − 8y = −25 SOLUTION: Page 27 Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the first equation by 4 and the second equation by −3, the coefficients of the y-terms are eSolutions Manual - Powered by Cognero Guide and Review - Chapter 6 Study The solution is (2, 5). 48. 11x − 6y = 3 5x − 8y = −25 SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the first equation by 4 and the second equation by −3, the coefficients of the y-terms are additive inverses. Now, substitute 3 for x in either equation to find y. The solution is (3, 5). 49. COINS Tionna has 25 coins in her piggy bank with a value of $4. The coins are either dimes or quarters. Define the variables, and write a system of equations to determine the number of dimes and quarters. Then solve the system using the best method for the situation. SOLUTION: Sample answer: Let d represent the number of dimes and let q represent the number of quarters. Use the fact that the value of a dime is $0.10 and the value of a quarter is $0.25 to write the equation for the value. d + q = 25 0.10d + 0.25q = 4 Because the coefficients of d and q in the first equation are 1, the best method is substitution. Solve the first equation for q. q = −d + 25 Substitute −d + 25 for q in the second equation. Substitute 15 for d in either equation to find q. eSolutions Manual - Powered by Cognero The solution is (15, 10). Page 28 Study Guide and Review - Chapter 6 The solution is (3, 5). 49. COINS Tionna has 25 coins in her piggy bank with a value of $4. The coins are either dimes or quarters. Define the variables, and write a system of equations to determine the number of dimes and quarters. Then solve the system using the best method for the situation. SOLUTION: Sample answer: Let d represent the number of dimes and let q represent the number of quarters. Use the fact that the value of a dime is $0.10 and the value of a quarter is $0.25 to write the equation for the value. d + q = 25 0.10d + 0.25q = 4 Because the coefficients of d and q in the first equation are 1, the best method is substitution. Solve the first equation for q. q = −d + 25 Substitute −d + 25 for q in the second equation. Substitute 15 for d in either equation to find q. The solution is (15, 10). So, Tionna has 15 dimes and 10 quarters in her piggy bank. 50. FAIR At a county fair, the cost for 4 slices of pizza and 2 orders of French fries is $21.00. The cost of 2 slices of pizza and 3 orders of French fries is $16.50. To find out how much a single slice of pizza and an order of French fries costs, define the variables and write a system of equations to represent the situation. Determine the best method to solve the system of equations. Then solve the system. SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the second equation by -2, the coefficients of the p -terms are additive inverses. Now, substitute 3 for f in either equation to find p . eSolutions Manual - Powered by Cognero Page 29 The solution (15, 10).- Chapter 6 Study Guide andisReview So, Tionna has 15 dimes and 10 quarters in her piggy bank. 50. FAIR At a county fair, the cost for 4 slices of pizza and 2 orders of French fries is $21.00. The cost of 2 slices of pizza and 3 orders of French fries is $16.50. To find out how much a single slice of pizza and an order of French fries costs, define the variables and write a system of equations to represent the situation. Determine the best method to solve the system of equations. Then solve the system. SOLUTION: Because none of the coefficients are 1 or −1, elimination using multiplication is the best method. Notice that if you multiply the second equation by -2, the coefficients of the p -terms are additive inverses. Now, substitute 3 for f in either equation to find p . pizza: $3.75; French fries: $3 Solve each system of inequalities by graphing. 51. x > 3 y <x+2 SOLUTION: Graph each inequality. The graph of x > 3 is dashed and is not included in the graph of the solution. The graph of y < x + 2 is also dashed and is not included in the graph of the solution. eSolutions Manual - Powered by Cognero Page 30 The solution of the system is the set of ordered pairs in the intersection of the graphs of x > 3 and y < x + 2. Overlay the graphs and locate the green region. This is the intersection. Study Guide and Review - Chapter 6 pizza: $3.75; French fries: $3 Solve each system of inequalities by graphing. 51. x > 3 y <x+2 SOLUTION: Graph each inequality. The graph of x > 3 is dashed and is not included in the graph of the solution. The graph of y < x + 2 is also dashed and is not included in the graph of the solution. The solution of the system is the set of ordered pairs in the intersection of the graphs of x > 3 and y < x + 2. Overlay the graphs and locate the green region. This is the intersection. The solution region is shaded in the graph below. 52. y ≤ 5 y >x−4 eSolutions Manual - Powered by Cognero SOLUTION: Graph each inequality. Page 31 Study Guide and Review - Chapter 6 52. y ≤ 5 y >x−4 SOLUTION: Graph each inequality. The graph of y ≤ 5 is solid and is included in the graph of the solution. The graph of y > x − 4 is dashed and is not included in the graph of the solution. The solution of the system is the set of ordered pairs in the intersection of the graphs of y ≤ 5 and y > x − 4. Overlay the graphs and locate the green region. This is the intersection. The solution region is shaded in the graph below. 53. y < 3x − 1 y ≥ −2x + 4 eSolutions Manual - Powered by Cognero SOLUTION: Graph each inequality. Page 32 Study Guide and Review - Chapter 6 53. y < 3x − 1 y ≥ −2x + 4 SOLUTION: Graph each inequality. The graph of y < 3x − 1 is dashed and is not included in the graph of the solution. The graph of y ≥ −2x + 4 is solid and is included in the graph of the solution. The solution of the system is the set of ordered pairs in the intersection of the graphs of y < 3x − 1 and y ≥ −2x + 4. Overlay the graphs and locate the green region. This is the intersection. The solution region is shaded in the graph below. 54. y ≤ −x − 3 y ≥ 3x − 2 eSolutions Manual - Powered by Cognero SOLUTION: Graph each inequality. Page 33 Study Guide and Review - Chapter 6 54. y ≤ −x − 3 y ≥ 3x − 2 SOLUTION: Graph each inequality. The graph of y ≤ −x − 3 is solid and is included in the graph of the solution. The graph of y ≥ 3x − 2 is also solid and is included in the graph of the solution. The solution of the system is the set of ordered pairs in the intersection of the graphs of y ≤ −x − 3 and y ≥ 3x − 2. Overlay the graphs and locate the green region. This is the intersection. The solution region is shaded in the graph below. 55. JOBS Kishi makes $7 an hour working at the grocery store and $10 an hour delivering newspapers. She cannot work more than 20 hours per week. Graph two inequalities that Kishi can use to determine how many hours she needs to work at each job if she wants to earn at least $90 per week. eSolutions Manual - Powered by Cognero SOLUTION: Let g represent the number of hours Kishi works at the grocery store. Let n represent the number of hours she Page 34 Study Guide and Review - Chapter 6 55. JOBS Kishi makes $7 an hour working at the grocery store and $10 an hour delivering newspapers. She cannot work more than 20 hours per week. Graph two inequalities that Kishi can use to determine how many hours she needs to work at each job if she wants to earn at least $90 per week. SOLUTION: Let g represent the number of hours Kishi works at the grocery store. Let n represent the number of hours she spends delivering newspapers. Write a system of inequalities. 7g +10n ≥ 90 g + n ≤ 20 Graph each inequality. The graph of 7g +10n ≥ 90 is solid and is included in the graph of the solution. The graph of g + n ≤ 20 is also solid and is included in the graph of the solution. The solution of the system is the set of ordered pairs in the intersection of the graphs of 7g +10n ≥ 90 and g + n ≤ 20. Overlay the graphs and locate the green region. This is the intersection. The Manual solution region by is Cognero shaded eSolutions - Powered in the graph below. Page 35 Study Guide and Review - Chapter 6 The solution region is shaded in the graph below. eSolutions Manual - Powered by Cognero Page 36