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Name _______________________________________ Date __________________ Class __________________ UNIT 3 Solving Equations and Systems of Equations Unit Test: B 1. Jake and Hannah wash windows. Jake charges $50 plus $2 per window. Hannah charges $20 plus $5 per window. For how many windows washed do they charge the same amount? A 7 windows C 15 windows B 10 windows D 70 windows 6. Solve this system by graphing both equations. Use the grid below. y 2 x 6 y 4x Which point is the solution? 2. A red car and a blue car are traveling at the same speed. The red car drives 3 hours. The blue car drives another half hour and goes 25 more miles. Which equation can be solved to find how fast the cars are going? A 3x 25 3.5x C 2.5x 25 3x B 3x 25 2.5x D 3.5x 25 3x 3. Anna and David left an 18% tip after having dinner at a restaurant. The amount of the tip was $9. Anna’s dinner cost $28. Which equation can you use to find x, the cost of David’s dinner? A 0.18(x 28) 9 C 18(x 28) 9 B 0.18x 28 9 D 0.18x 28 9 A (1, 4) C (1, 4) B (1, 4) D (1, 4) 7. Which expression can you substitute in the indicated equation to solve the system below? x 9y 6 12 x y 5 4. For the equation 3(7 x) 3x k, which value of k will create an equation with no solutions? A 5 12x for y in x 9y 6 B 5 x for y in x 9y 6 A x C 15 C 6 9y for x in 12x y 5 B 3x D 21 D 6 9y for x in 12x y 5 5. Which step could you use to start solving the system of equations below? x 3 y 15 8. Which is the solution to ? x 7y 5 2 x 5 y 1 8 x 4 y 16 A Substitute 5y 1 for x in 8x 4y 16. A (9, 2) C (2, 9) B (9, 2) D (2, 9) 9. The graph of a system of two linear equations is a pair of lines that intersect at the origin. Which statement is true of the system? B Multiply 2x 5y 1 by 4 and subtract it from 8x 4y 16. C Multiply 2x 5y 1 by 4 and add it to 8x 4y 16. A The solution is zero. D Add 2x 5y 1 to 8x 4y 16. C The system has no solution. B The solution is (0, 0). D The system has infinitely many solutions. Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 1 Name _______________________________________ Date __________________ Class __________________ UNIT 3 Solving Equations and Systems of Equations 10. A train leaves Buffalo traveling west at 60 miles per hour. An hour later, another train leaves Buffalo traveling east at 80 miles per hour. When are the two trains the same distance from Buffalo? Show the equation you use. 15. Art bought $100 worth of stock and gained $25 per year. Kiley bought $400 worth of another stock and lost $35 per year. Use x for time and y for stock value. Write and graph equations to represent each situation. When did Art and Kiley have the same amount of stock value? equation: _________________________________ Art: ___________________________________ answer: __________________________________ Kiley: ___________________________________ 11. A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off the ground and rises at 1.5 meters per second. Write and solve an equation to determine when the balloons are at the same height. equation: _________________________________ answer: _________________________________ answer: __________________________________ 16. Determine the expression you can substitute for x in 4x 2y 3 to solve the system below. 12. Nina saves 40% of her summer job earnings for college. This summer, she earned $200 more than last summer, and she saved $900. Write and solve an equation to find her earnings last summer. 4 x 2y 3 6y 4 x ________________________________________ 17. Find the solution to the system of equations below. equation: _________________________________ 2y 5 x 7 5 x 3 y 2 solution: _________________________________ 13. Complete the equation so it has infinitely many solutions. ________________________________________ 3(2 x) 3x_________________ 18. The graph of a system of two equations is a pair of parallel lines. Does the system have a solution? Explain. 14. At the museum, the O’Rourke family bought 3 adult tickets and 2 children’s tickets for $23.50. The Patel family bought 2 adult tickets and 4 children’s tickets for $25. Find the cost of each type of ticket. ________________________________________ ________________________________________ _______________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 96