Lesson 5.5 Inconsistent and Dependent Systems of Linear Equations
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1 Name: Date: Lesson 5.5 Inconsistent and Dependent Systems of Linear Equations Graph the system of linear equations on a coordinate grid. State whether the system of equations is inconsistent or dependent. 1. 5x 2y x 4y 20 10x 4y 22 3x y 5 Graph the system of linear equations on a graphing calculator. State whether the system of linear equations is inconsistent or dependent. 3. 2x y x 2y 5 5y 10x 5 10x 10y 45 Extra Practice Course 3A 95
2 Name: Date: State whether each system of linear equations is inconsistent, dependent, or has a unique solution. Justify each answer. Solve each system of linear equations if possible. 5. 8x 4y x 3y 9 2x y 28 4x y x 8y x 4y 22 6x 2y 17 6x 8y x 9y x 5y 17 16x 36y 28 2x 10y x 36y x 3y 5 6x 18y 27 14x 21y Chapter 5 Lesson 5.5
3 Name: Date: Solve. Show your work. 13. Melissa reserved a two-night stay at a lodge inclusive of 3 meals for $185. Angela reserved the same lodge for a four-night stay, inclusive of 6 meals for $350. a) Write a system of linear equations to find the cost of a one-night stay and one meal at the lodge. b) State with reasons whether the system of equations has a unique solution, is inconsistent, or is independent. c) What does this tell you about the reservations made by Melissa and Angela? 14. Mr. Henderson bought some wooden planks of different lengths. Length of A 2 length of B A B C D Length of D 2 length of C When he places planks A and D end-to-end, the total length is 16 inches. When he places planks B and C end-to-end, the total length is 8 inches. a) Write a system of equations to find the length of the wooden plank B and the length of wooden plank C. b) State with reasons whether the system of equations has a unique solution, is inconsistent, or is independent. Extra Practice Course 3A 97
4 10. a) Note: In your graphing calculator, Y represents C. Lesson x 1 2y 5 16 x y x 1 4y 5 22 x y y 8 b) 15 campers 11. a) Note: In your graphing calculator, Y represents D x 2y x 4y x 2 The system of linear equations is b) The two vehicles will meet 2 hours later. 12. a) Note: In your graphing calculator, Y represents L. b) 2 pounds of weight attached to each spring will result in the springs stretching the same number of inches. Extra Practice Course 3A 183
5 2. 12x 1 4y x y x 1 y 5 5 x y y x 4y 20 or 3x y The The system of linear equations is not dependent. It has a unique solution. x The system of linear equations is 5. 8x 1 4y x 1 4y 2 8x x 4y x y x So the equation has slope 22 and y-intercept x 1 y x 1 y 2 2x x y x So the equation has slope 22 and y-intercept 28. When the two graphs have the same slope and different intercepts, they are parallel. The system of linear equations is 6. 12x 2 3y x 2 3y 2 12x x 23y x 3y 512x 2 9 y 5 4x 2 3 So the equation has slope 4 and y-intercept 23. 4x 2 y 5 3 4x 2 y 2 4x x 2y x y 5 4x 2 3 So the equation has slope 4 and y-intercept Answers
6 7. 224x 1 8y x 1 8y 2 (224x) (224x) 8y x y x So the equation has slope 3 and y-intercept x 1 2y x 1 2y 2 (26x) (26x) 2y x y x So the equation has slope 3 and y-intercept 8.5. When the two graphs have the same slope and different intercepts, they are parallel. The system of linear equations is 8. 3x 1 4y x 1 4y 2 3x x 4y x y x So the equation has slope and y-intercept x 2 8y x 2 8y 2 6x x 28y x y x So the equation has slope 0.75 and y-intercept The two graphs have different slopes and y-intercepts. The system of linear equations has a unique solution. 9. 4x 1 9y 5 7 4x 1 9y 2 4x x 9y x 7 4x y 9 9 So the equation has slope and y-intercept x 1 36y x 1 36y 2 16x x 36y x y So the equation has slope and y-intercept x 1 5y 5 17 x 1 5y 2 x x 5y x y x So the equation has slope 20.2 and y-intercept x 1 10y x 1 10y 2 2x x 10y x y x So the equation has slope 20.2 and y-intercept 1.1. When the two graphs have the same slope and different intercepts, they are parallel. The system of linear equations is x 1 36y x 1 36y 2 12x x 36y x y x So the equation has slope and y-intercept x 1 18y x 1 18y 2 6x x 18y x y x So the equation has slope and y-intercept x 1 3y 5 5 2x 1 3y 2 2x x 3y x y x So the equation has slope and y-intercept x 1 21y x 1 21y 2 14x x 21y x y x So the equation has slope and y-intercept 5 3. Extra Practice Course 3A 185
7 13. a) Let the cost of a one-night stay be n and the cost of one meal be m. 2n 1 3m Equation 1 4n 1 6m Equation 2 b) 2n 1 3m n 1 3m 2 2n n 3m n m n 4n 1 6m n 1 6m 2 4n n 6m n m n The equations have the same slope and but different vertical intercepts. The system of linear equations is c) The package Angela reserved to stay at the lodge has the least cost per day. 14. a) Let the length of plank B be x and the length of plank C be y. Length of plank A 5 2x Length of plank D 5 2y 2x 1 2y 5 16 Equation 1 x 1 y 5 8 Equation 2 b) 2x 1 2y 2 2x x 2y x y x So, the equation has slope 21 and y-intercept 8. x 1 y 2 x x y x So, the equation has slope 21 and y-intercept 8. The two equations represent the same line. The system of equations is dependent. Brain@Work 1. Let x be the tens place value of the number and y be the unit value of the number. x 1 y 5 11 Equation 1 10y 1 x 2 (10x 1 y) y 2 y 1 x 2 10x 5 9 9y 2 9x 5 9 y 2 x 5 1 Equation 2 Add Equation 1 and Equation 2: x 1 y 1 y 2 x y 5 12 y 5 6 Substitute y 5 6 into Equation 1: x x 5 5 So the number is (x 2 2) x 24x x 24x x x 5 22x x 1 4x 5 22x x 2x x 5 6 x (y 2 3) 2 3(y 2 2) y y y y 5 28 y 5 8 z z z 2 3 z Answers
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