Solving Equations and Systems of Equations

Name______Date______Class______UNIT Solving Equations and Systems of Equations 3 Unit Test: B

1. Jake and Hannah wash windows. Jake 6. Solve this system by graphing both charges $50 plus $2 per window. Hannah equations. Use the grid below. charges $20 plus $5 per window. For how y= -2 x + 6 many windows washed do they charge the same amount? y= 4 x A 7 windows C 15 windows Which point is the solution? B 10 windows D 70 windows A (1, 4) C (1, 4) 2. A red car and a blue car are traveling at B (1, 4) D (1, 4) 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 7. Which expression can you substitute in cost $28. Which equation can you use to the indicated equation to solve the find x, the cost of David’s dinner? system below? A 0.18(x  28)  9 C 18(x  28)  9 x+9 y = 6 B 0.18x  28  9 D 0.18x  28  9 12x+ y = 5 4. For the equation 3(7  x)  3x  k, which A 5  12x for y in x+9 y = 6 value of k will create an equation with no x+9 y = 6 solutions? B 5  x for y in 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 -x +3 y = 15 8. Which is the solution to ? the system of equations below? x+7 y = 5 2x+ 5 y = 1 A (9, 2) C (2, 9) 8x+ 4 y = 16 B (9, 2) D (2, 9) A Substitute 5y - 1 for x in 9. The graph of a system of two linear 8x  4y  16. equations is a pair of lines that intersect B Multiply 2x+ 5 y = 1 by 4 and at the origin. Which statement is true of subtract it from 8x  4y  16. the system? C Multiply 2x+ 5 y = 1 by 4 and add it A The solution is zero. to 8x  4y  16. B The solution is (0, 0). D Add 2x+ 5 y = 1 to 8x  4y  16. CThe system has no solution. D The system has infinitely many solutions.

UNIT Solving Equations and Systems of Equations 3

10. A train leaves Buffalo traveling west at 15. Art bought $100 worth of stock and 60 miles per hour. An hour later, another gained $25 per year. Kiley bought $400 train leaves Buffalo traveling east at worth of another stock and lost $35 per 80 miles per hour. When are the two year. Use x for time and y for stock value. trains the same distance from Buffalo? Write and graph equations to represent Show the equation you use. 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 12. Nina saves 40% of her summer job system below. earnings for college. This summer, she earned $200 more than last summer, and 4x+ 2 y = 3 she saved $900. Write and solve an 6y= 4 - x equation to find her earnings last ______summer. 17. Find the solution to the system of equation: ______equations below. 2y= 5 x - 7 solution: ______5x+ 3 y = 2 13. Complete the equation so it has infinitely ______many solutions. 18. The graph of a system of two equations is a pair of parallel lines. Does the system 3(2  x)  3x______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. ______