NAME
DATE
CORE
Final Answers
Math 8 Unit 4 Test
1 a)______________
1. Solve each equation showing ALL work! If necessary, answer as
ALL solutions or NO solution. If it has ONE solution, check your answer.
x
𝑎) 8𝑥 + 5 = 29
b) −4𝑛 − 5 = 15
c) 6 + 8 = 28
b)________________
c)________________
d)________________
e)________________
Check:
d) 2𝑥 + 2 = 𝑥 + 5
Check:
Check:
𝑒) 8(2𝑐 − 3) = 4(4𝐶 − 8)
f)________________
g)________________
2 a)_____________________
b)___________________
c)____________________
3 a)_______________________
b)____________________
Check:
f) 2𝑛 + 5 = −5𝑛 + 5
Check:
g) 5𝑑 + 4 − 2𝑑 − 10 = 3(𝑑 − 2)
c)____________________
4 a)_____________________
b)____________________
c)_____________________
5)_______________________
6)_______________________
7)_______________________
Check:
Check:
8)_______________________
*Bonus)______________
2) State whether each equation has ONE solution, NO solution, or All numbers (Infinite) solutions.
𝑎) 7ℎ − 3 = −3 + 7ℎ
𝑏) 7ℎ − 3 = 3 − 7ℎ
𝑐) 3 + 7ℎ = 7ℎ − 3
3. Andre and Elena are each saving money. Andre starts with $100 in his savings account and adds
$5 per week. Elena starts with $10 in her savings account and adds $20 each week.
a) After how many weeks will Andre and Elena have the same amount of money in their
savings accounts? Write & solve an equation. (Hint: Andre’s total savings should be equal to
Elena’s total savings.)
Equation: _____________________ = ____________________________
b) How much money do they both have after this number of weeks?
c) Complete the table below. After 4 weeks, who has more money in their savings account?
Week
0
1
2
3
4
5
6
Andre total $
Elena total $
4. Find the solution to each system of equations by graphing. Write your solution in the answer column.
a.
𝑦 = 2𝑥 − 3
𝑦 =𝑥+2
b.
𝑦 = 2𝑥 − 4
𝑦=
1
𝑥+3
4
c.
𝑦 = −2𝑥 + 4
𝑦 = −2𝑥 − 6
5. Which system of equations has exactly one solution?
A. {
𝑦 = −𝑥 + 10
𝑦 = −𝑥 + 10
B. {
𝑦 = −2𝑥 + 1
𝑦 = −2𝑥 + 6
C. {
𝑦 = 3𝑥 + 1
𝑦 = 3𝑥 − 7
D. {
𝑦 = 3𝑥 + 1
𝑦 = −3𝑥 + 7
6. Write a second equation to create a system of equations which has no solution:
𝑦=
2
5
𝑥+7
7. The solution to a system of equations is (6, −2). Which equation below could be the other equation
in the system? Hint: “Which equation does (6, -2) satisfy?”
A.
1
𝑦 = 2𝑥 − 5
B. 𝑦 = 2𝑥 − 15
C. 𝑦 = −3𝑥 + 14
D.
𝑦=
−1
3
𝑥+4
8. How many solutions does the following system have?
y = -2x + 5
y = -2x + 5
A. NO solutions
B. ALL numbers
C. ONE solution
D. Parallel
*Bonus: At what coordinate would the graphs of the following equations intersect?
4x + y = -3
2x + 5y = -15