Review: Algebra 1
Systems of Equations
Test Date: Dec. 6, 2016
1. What is the value of y in the solution of the following systems?
𝑦 = 2𝑥 − 1
a. {
}
2𝑥 + 2𝑦 = 22
2𝑥 + 𝑦 = −12
b. {
}
−4𝑥 − 2𝑦 = 30
2. What is the value of x in the solution of the following systems?
3𝑥 = 2𝑦 + 14
a. {
}
𝑦 = −6𝑥 + 18
3. What is the solution to the following systems?
−𝑥 + 𝑦 = −13
a. {
}
3𝑥 − 𝑦 = 19
15𝑥 − 12𝑦 = 13
b. {
}
30𝑥 + 9𝑦 = 4
𝑥 + 2𝑦 = 23
b. {
}
5𝑥 + 10𝑦 = 55
4. Find the solution to the following problems (you need to make a system of equations)
and tell what each number in the solution represents.
a. The owner of a hair salon charges $20 more per haircut than the assistant.
Yesterday the assistant gave 12 haircuts. The owner gave 6 haircuts. The total
earnings from haircuts were $750. How much does the owner charge for a
haircut?
b. It takes a florist 3 hours and 15 minutes to make 3 small centerpieces and 3 large
centerpieces. It takes 6 hours and 20 minutes to make 4 small centerpieces and 7
large centerpieces. How long does it take to make each small centerpiece and
each large centerpiece?
5. A new spiral notebook contains 30 more sheets of paper than a new memo book. The
total number of sheets of paper in 3 new spiral notebooks and 5 new memo books is
810. Which system of equations can be used to find s, the number of sheets of paper in
one new spiral notebook, and m, the number of sheets of paper in one new memo
book?
𝑠 − 𝑚 = 30
a. {
}
3𝑠 + 5𝑚 = 810
𝑠 − 𝑚 = 30
c. {
}
5𝑠 + 3𝑚 = 810
𝑠 + 𝑚 = 30
b. {
}
3𝑠 + 5𝑚 = 810
𝑠 + 𝑚 = 30
d. {
}
5𝑠 + 3𝑚 = 810
Review: Algebra 1
Systems of Equations
Test Date: Dec. 6, 2016
6. The owner of a clothing store buys T-shirts for c dollars each and sells them for p dollars
each. Last month she bought 600 T-shirts and sold 500 of them and made a profit of
$2,800. This month she bought 400 T-shirts and sold them all and made a profit of
$2,400. Which system of equations can be used to determine the values of c and p?
500𝑝 − 600𝑐 = 2,800
a. {
}
400𝑝 − 400𝑐 = 2,400
500𝑝 − 600𝑐 = 2,800
c. {
}
400𝑝 − 𝑐 = 2,400
600𝑝 − 500𝑐 = 2,800
b. {
}
400𝑝 − 400𝑐 = 2,400
600𝑝 − 500𝑐 = 2,800
d. {
}
400𝑝 − 𝑐 = 2,400
7. A carpenter makes and sells rocking chairs. Using either the graph provided or another
method of solving a system, tell how many chairs he must sell for his expenses to equal
his income.
Expense: y = 15x + 420
Income: y = 75x
Hint: Would another way of
solving save you time?
8. How does a graph representing a system of equations with no solution look? How does
a graph representing a system of equations with infinite solutions look? Describe.
9. What is the solution of the system pictured?
6x + 3y = 18
x
0
1
2
3
4
5
6
y
-9
-6
-3
0
3
6
9
Review: Algebra 1
Systems of Equations
10. Find and describe the error in the system solved below.
a.
b.
c.
d.
Test Date: Dec. 6, 2016