Name
Date
Hour
Score
R.7 Unit 7 Complete Review- you may need to show your work on a separate piece of paper
Graph each system of equations using a ruler. Determine whether the system has no solution, one
solution, or infinitely many solutions. If the system has one solution, estimate the solution.
y
1. y= –x – 3
2. y = ¼x + 2
y
y=x–1
4y = x
x
x
3. y = x – 1
y–x=-1
4. y = x + 1
3x + 3y = –3
y
x
y
x
Determine the best method to solve each system of equations. Then solve the system.
5. y = 6x
(Substitution)
6. x = 3y
(Substitution)
7. x = 2y + 7 (Substitution)
2x + 3y = –20
3x – 5y = 12
x=y+4
8. y = 2x – 2
y=x+2
(Substitution)
9. y = 2x + 6 (Substitution)
2x – y = 2
11. x + y = –4
x–y=2
(Addition)
12. 6x + 5y = 4 (Subtraction)
6x – 7y = –20
13. 3c + d = 4 (Addition)
2c – d = 6
15. 2x + y = 0 (Elimination)
5x + 3y = 2
16. 3x – 6y = –3 (Elimin.)
2x + 4y = 30
14. x + y = –9 (Elimination)
5x – 2y = 32
10. 3x + y = 12 (Substitution)
y = –x – 2
Determine the best method to solve each system of equations. Then solve the system.
17. 5x + 7y = 3
18. 7x + 2y = 2
19. x = 2y + 6
2x – 7y = –38
2x – 3y = –28
½x – y = 3
For the following stories write the two corresponding equations and find the solution to the system.
20. The sum of two numbers is 16 and their difference is 20. What are the two numbers?
21. Jon is older than Richard. The sum of their two ages is 58 and the difference of their ages is 2.
Find the age of each.
22. An airport shuttle company owns sedans that have a maximum capacity of 3 passengers and
vans that have a maximum capacity of 8 passengers. Their 12 vehicles have a combined maximum
capacity of 61 passengers. How many sedans and vans does the company own?
For problems 23 and 24, without graphing decide whether the following systems of equations
has one solution, no solutions, or infinitely many solutions.
23.
y = 2x + 3
y = 4x + 1
24. y = 9x + 2
y = 9x –3
23. ________________________
24. ________________________
25. Is (2,1) a solution of the system
of linear equations?
-7x + y = -13
x+y=3
26.
25. ________________________
Determine which of the following represents a system of linear equations. Circle all that apply.
A. x = -9
B. z = 7x
C. 6xz + 7
D. 17x = 36 - 24z
z = -9 + x
z = 2.7x
14 x + 21 y - 16