Algebra 1 Systems of Equations Review
Name ______________________
1. Identify the graph that represents the system of linear equations.
y=x
3x - 10y = - 14
A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4
2. Identify the graph that represents the system of linear equations.
y-x+6=0
2x = 2y + 12
A. Graph 1
B. Graph 2
C. Graph 3
D. Graph 4
3. The graph below represents the relationship between the cost of riding in a cab and how many miles you
travel. The Yellow Cab Company charges a $2 fee plus $2 per mile. The Blue Cab Company charges a fee of $5
plus $1 per mile.
a.) Write the system of equations for this problem.
Equation 1 ________________________________
Equation 2_________________________________
b.) At what number of miles is the cost for each
company the same?
c.) What is the cost when they are the same?
4. Solve the following system of equations using a table and a graph. Circle the solution on the table and the
graph.
y = 2x – 3
3x + y = 2
X
Y
X
The solution is:
X = ______, Y = _______
Y
5. A large group of students wants to go to the movies. If the students take 3 vans and 1 car, they can
transport 22 people. If they take 2 vans and 4 cars, they can transport 28 people. Write and solve a system of
equations to find the number of people that can be transported a van.
6. One thousand eight hundred seventy tickets were sold for the carnival on Saturday. Each adult ticket cost
$5.50, and each student ticket cost $4.00. The total revenue for ticket sales was $9,166. Identify the pair of
equations that do not represent the number of a (adult) tickets and s (student) tickets.
A.
1,870 – s = a
5. 5a + 4s = 9,166
B.
1,870 – a = s
5.5a + 4s = 9,166
C.
9,166 + 5.5a = 4s
a + s = 1,870
D.
1,870 + 5.5a = 4s
5.5a + 4s = 9,166
7. A basketball team scored 38 field goals in their game for a total of 85 points. Field goals are worth two or
three points depending on how far out the shooter is from the basket. Which system of equations below
could be used to solve for x, the number of three-point shots, and y, the number of two-point field goals?
A.
x + y = 85
3x + 2y = 38
C.
x + y = 38
2x + 3y = 85
B.
2x + 3y = 38
x + y = 85
D.
x + y = 38
3x + 2y = 85
8. The cheerleaders collected change to help buy new uniforms. Their collection had a total of 432 dimes and
nickels. The total value of the coins is $. Use a system of equations to find the number of dimes and nickels
they collected.
x _________________________
Equation 1 ___________________________
# of Dimes _______
y _________________________
Equation 2 ___________________________
# of Nickels _______
9. A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70.
The total number of mowers sold was 30. The small mowers cost $249.99. The large mowers cost $329.99.
Find the number of each type of mower sold.
x ____________________
Equation 1 ___________________________
# of small mowers _______
y ____________________
Equation 2 ___________________________
# of large mowers _______
10. Analyze the data in the table (X, Y1).
X
-1
0
1
2
One of the tables below (X, Y2) is not a solution to (X, Y1).
Identify the table below that does not represent a solution
to the system (X, Y1).
a.)
b.)
X
-1
0
1
2
Y2
-6
-1
4
9
c.)
X
-1
0
1
2
Y2
1
4
7
10
Y1
-2
1
4
7
d.)
X
-1
0
1
2
Y2
-2
2
6
10
X
-1
0
1
2
Y2
0
1
2
3
11. The perimeter of a rectangle is 20 inches. The length of the rectangle is one more than twice its width.
What is the area of the rectangle?
12. A rectangle has a perimeter of fifty-eight inches. The length is one more than three times the width.
Write and solve a system of linear equations to find the length and width of the rectangle.
13. The area of a rectangle is 244 centimeters squared. The length is four times longer than it wide. Which
system of equations could be used to find out the length and width of the rectangle?
A.
xy = 244
x = 4y
C.
xy = 244
244 = 2x + 2y
B.
y = 4x
244x = y
D.
xy = 244
2(x + y) = 4
14. Which system describes the following situation: The sum of two numbers is 20. The difference between
three times the larger and twice the smaller is 40.
A.
x + y = 20
3x + 2y = 40
C.
x + y = 20
3x – 2y = 40
B.
x – y = 20
3x – 2y = 40
D.
x – y = 20
3x + 2y = 40
15. Which system of equations describes the following situation? Craig has $0.80 in nickels and dimes. He has
four more nickels than dimes.
A.
x+y=4
10x + 5y = 80
C.
x–y=4
10x + 5y = 80
B.
y–x=4
10x + 5y = 80
D.
x+y=4
10x – 5y = 80