Download Name Date Class Solving Equations and Systems of Equations Unit

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