WorksheetsSolving systems of equations
Total questions: 40
Worksheet time: 52mins
Name
Class
Date
1.
Solve for x and y.
y = 2/3x - 2
y = -x + 3
y = 2/3x - 2
y = -x + 3
a)
(0,3)
b)
(0,-3)
c)
(3,0)
d)
(-3,0)
2.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
3.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
4.
What is the solution?
a)
(1, -1)
b)
(-1, 1)
c)
(0, -2)
d)
(2, 0)
5.
This system has _____ solutions
a)
0
b)
1
c)
2
d)
Infinitely many
6.
a)
Infinitely Many Solutions
b)
No Solution
7.
Solve the system of equations.
x + 2y = -3
x - y = -12
x + 2y = -3
x - y = -12
a)
(-9, 3)
b)
(-7 ,5)
c)
(3, 15)
d)
(9, 6)
8.
Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0
−4x − 4y = 0
4x + 4y = 0
a)
(−6, −4)
b)
Infinite number of solutions
c)
(−6, 10)
d)
(6, 4)
9.
1) -4x-2y=-12
4x+8y=-24
4x+8y=-24
a)
(6,-6)
b)
(-6,6)
c)
(6,6)
d)
(-6,-6)
10.
How many solutions does the following equation have?
3x − 3 = −3 + 3x
3x − 3 = −3 + 3x
a)
One Solution
b)
No Solutions
c)
Infinitely Many Solutions
11.
In a pasture are horses and chickens if there are a total of 28 animals and 80 legs how many chickens and horses?
a)
10 horses, 18 chickens
b)
16 horses, 12 chickens
c)
12 horses, 16 chickens
d)
18 horses, 10 chickens
12.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
y = 2x - 3
b)
x + y = 33
x = 2y - 3
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
x = 33 - 2y
13.
The equations of two lines are:
2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?
a)
x=8
b)
x=3
c)
x=11
d)
x=5
14.
Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?
a)
x+y=134
x+y=120
x+y=120
b)
3x+3y=134
4x+3y=120
4x+3y=120
c)
4x+3y=134
3x+3y=120
3x+3y=120
d)
7xy=134
6xy=120
6xy=120
15.
Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?
a)
$5
b)
$10
c)
$15
d)
$20
16.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
1.5x+0.5y=78.5
x+y=87
x+y=87
b)
1.5x+0.5y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
c)
x+y=78.5
1.5x+0.5y=87
1.5x+0.5y=87
d)
x+y=78.5
x+y=87
x+y=87
17.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
18.
Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
19.
What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7
x-2y=1
x+4y=7
a)
1
b)
-1
c)
3
d)
4
20.
Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.
WRITE a system where T= # of $20 and F = # of $50.
a)
T + F = 1430
20T + 50F = 49
20T + 50F = 49
b)
T+ F = 49
10T + 5F = 1430
10T + 5F = 1430
c)
T + F = 49
20T + 50F = 1430
20T + 50F = 1430
d)
T + F = 49
T + F = 1430
T + F = 1430
21.
Is (-3, 1) a solution to the system:
x + y = -2
2x - 2y = -8
a)
Yes, (-3, 1) is the solution
b)
No, (-3, 1) is the solution
22.
Is (-1, 1) a solution to the system:
x + y = 0
3x - 3y = 0
a)
Yes, (-1, 1) is the solution
b)
No, (-1, 1) is the solution
23.
Is (1, 2) a solution to the system:
3x - 2y = 1
x + 4y = 9
a)
Yes, (1, 2) is the solution
b)
No, (1, 2) is the solution
24.
What is the solution to:
y = x + 2
y = -x
a)
(-1,1)
b)
(2, -1)
c)
(1, -1)
d)
(0, 2)
25.
What is the solution to
y = x - 2
y = -x + 2
a)
(0, 2)
b)
(-2, 2)
c)
(1, -1)
d)
(2, 0)
26.
What is the solution to
y = 6
y = 1
a)
(0, 0)
b)
(6, 1)
c)
No solution
d)
Infinity many solutions
27.
What is the x-value to the solution?
y = -2x + 4
y = -2
a)
4
b)
3
c)
-2
d)
-6
28.
What is the solution to
y = x - 4
2x - 3y = -2
a)
No solution
b)
(-4, -2)
c)
(10, 14)
d)
(14, 10)
29.
What is the y-value of the solution to the system
5x - 3y = 1
x = -4y - 9
a)
-1
b)
-2
c)
-3
d)
-4
30.
What is the solution of the system?
-x + y = 1
x + y = 1
a)
(0, 1)
b)
(1, 0)
c)
(-1, 0)
d)
(1 ,1)
31.
What is the y-value to the system below?
5x + 3y = 6
-3x - 3y = 6
a)
-3
b)
3
c)
6
d)
-8
32.
The difference of a and b is 3. The sum of the variables is 13. Find the numbers.
a)
a = 7
b = 10
b = 10
b)
a = 8
b = 5
b = 5
c)
a = 10
b = 13
b = 13
33.
Eight times a number increased by 9 is the same as 15 more than 7 times the number. Find the number.
a)
6
b)
-7
c)
1
d)
2
34.
Each of the equal sides of an isosceles triangle is 4 times the third side. The perimeter of the triangle is 114 inches. What would you label the three sides using the same variable.
a)
x, x , 4x
b)
x + 4, x+ 4, x
c)
x, x, x + 4
d)
x, 4x, 4x
35.
The length of a rectangle is 3 times the width. The perimeter of the rectangle is 72 feet. What is the area of the rectangle?
a)
243
b)
36
c)
9
d)
24
36.
Logan asked his 20 coworkers whether they own a car or a truck. There were 6 more car owners than truck owners. How many people owned a car?
a)
7 people
b)
9 people
c)
11 people
d)
13 people
37.
These two lines intersect at _____.
a)
(4, -2)
b)
(4, 2)
c)
(-2, 4)
d)
No solution
38.
The solution is:
a)
(4, 3)
b)
(3, 4)
c)
(-4, 3)
d)
No solution
39.
Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?
What is the solution?
a)
(-1, 4)
b)
(1, -4)
c)
(-4, 1)
d)
(4, -1)
40.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
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