Solving Equations and Systems of Equations

Name______Date______Class______

Solving Equations and Systems of Equations

Unit Test: B

Name______Date______Class______

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?

A7 windowsC15 windows

B10 windowsD70 windows

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?

A3x 25  3.5xC2.5x 25  3x

B3x 25  2.5xD3.5x 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?

A0.18(x28) 9 C18(x28) 9

B0.18x28 9D0.18x28 9

4.For the equation 3(7 x) 3xk, which value of k will create an equation with no solutions?

AxC15

B3xD21

5.Which step could you use to start solving the system of equations below?

ASubstitute for x in
8x 4y 16.

BMultiply by 4 and subtract it from 8x 4y 16.

CMultiply by 4 and add it to 8x 4y 16.

DAdd to 8x 4y 16.

6.Solve this system by graphing both equations. Use the grid below.

Which point is the solution?

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?

A5  12xfor y in

B5 x for y in

C6  9yfor x in

D6  9y for x in

8.Which is the solution to ?

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?

AThe solution is zero.

BThe solution is (0, 0).

CThe system has no solution.

DThe system has infinitely many solutions.

Name______Date______Class______

Solving Equations and Systems of Equations

Name______Date______Class______

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.

equation: ______

answer: ______

11.A red balloonstarts 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: ______

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.

equation: ______

solution: ______

13.Complete the equation so it has infinitely many solutions.

3(2 x)  3x______

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.

______

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?

Art:______

Kiley:______

answer:______

16. Determine the expression you can substitute for x in 4x 2y 3 to solve the system below.

______

17.Find the solution to the system of equations below.

______

18. The graph of a system of two equations is a pair of parallel lines. Does the system have a solution? Explain.

______