WorksheetsSystems of Equations
Total questions: 23
Worksheet time: 45mins
Name
Class
Date
1.
Solve by elimination
5x+6y= -10
3x-2y= -6
5x+6y= -10
3x-2y= -6
a)
(-2,0)
b)
(0,-2)
c)
(2,0)
d)
(0,2)
2.
Solve by elimination:
4x+9y=28
-4x-y=-28
4x+9y=28
-4x-y=-28
a)
(-7,0)
b)
(6,0)
c)
(-6,0)
d)
(7,0)
3.
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)
4.
Solve by elimination:
3x+7y=23
-3x-7y=-17
3x+7y=23
-3x-7y=-17
a)
No solution
b)
ARN
c)
(-3,3)
d)
(3,3)
5.
Solve by elimination
-12x-10y= 0
6x+5y= -1
-12x-10y= 0
6x+5y= -1
a)
infinite solutions
b)
(0,0)
c)
no solution
d)
(2,1)
6.
Solve by elimination
-2x+6y= 16
-4x-3y= 2
-2x+6y= 16
-4x-3y= 2
a)
(2,2)
b)
(-2, -2)
c)
(-2,2)
d)
(2,1)
7.
2x - y = 0
4x - y = 0
a)
(1,2)
b)
(0,0)
c)
No Solutions
d)
Infinite Solutions
8.
4x - 2y = 7
x + 2y = 3
What are x and y?
x + 2y = 3
What are x and y?
a)
x = 2, y = 2
b)
x = 1/2, y = 2
c)
x = 2, y = 1/2
d)
x = 2, y = -2
9.
If 3x - 2y = 14 and 2x + 2y = 6,
what are x and y?
what are x and y?
a)
x = 1, y = 2
b)
x = 2, y = 1
c)
x = -4, y = 1
d)
x = 4, y = -1
10.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
the same line (coinciding lines)
11.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?
a)
1s + 3c = 38
2s + 3c = 52
2s + 3c = 52
b)
3s + 1c = 38
3s + 2c = 52
3s + 2c = 52
c)
s + c = 38
s + c = 52
s + c = 52
d)
3s + 3c = 38
1s + 2c = 52
1s + 2c = 52
12.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?
a)
x + y = 1550
y = 4x
y = 4x
b)
x + y = 1550
y = x + 4
y = x + 4
c)
y - x = 1550
y = 4x
y = 4x
d)
y = 1550 + x
y = x + 4
y = x + 4
13.
Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?
a)
d + n = 6.60
.10d + .05n = 80
.10d + .05n = 80
b)
d + n = 80
d + n = 6.60
d + n = 6.60
c)
d + n = 80
.10d + .05n = 6.60
.10d + .05n = 6.60
d)
d + n = 80
.05d + .10n = 6.60
.05d + .10n = 6.60
14.
On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?
a)
10c + 5d = 14.25
5c + 10d = 16.50
5c + 10d = 16.50
b)
10c + 5d = 16.50
5c + 10d = 14.25
5c + 10d = 14.25
c)
c + d = 10
5c + 10d = 16.50
5c + 10d = 16.50
d)
c + d = 5
5c + 10d = 16.50
5c + 10d = 16.50
15.
A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?
a)
y = 6.80 + .65x
y=7.30+.90x
y=7.30+.90x
b)
x + y = 6.80
x + y = 7.30
x + y = 7.30
c)
y = 6.80+.90x
y = 7.30 + .65x
y = 7.30 + .65x
d)
y + .90x = 6.80
y + .65x = 7.30
y + .65x = 7.30
16.
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
a)
t + n = 54
t = 3n + 8
t = 3n + 8
b)
t + n = 54
n = 3t + 8
n = 3t + 8
c)
t + n = 54
t = 3n - 8
t = 3n - 8
d)
t + n = 8
t = 3n + 54
t = 3n + 54
17.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?
a)
y = 9.65 + x
y = 8.40 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
y = 8.40x - 58
18.
Solve the following system by graphing. What is the solution?
a)
(1, 2)
b)
(-1, 2)
c)
(2, 1)
d)
(2, -1)
19.
Solve using Elimination Method:
9x - 4y = 7
x - 4y = -17
a)
(-1,5)
b)
(-7,5)
c)
(7,5)
d)
(3,5)
20.
Solve for x
Hint: Solve using Elimination Method:
a)
4
b)
12
c)
-12 them together
d)
-4
21.
Solve the system:
2x + 3y = -2
3x - 2y = 23
2x + 3y = -2
3x - 2y = 23
a)
(5, -4)
b)
(-4, 5)
c)
(-5, 4)
d)
infinite solutions
22.
How can you use the substitution method to solve this system?
2x+7=y
4x+y=7
2x+7=y
4x+y=7
a)
Plug in 2x+7 in for 7 in second equation
b)
plug 2x+7 in for y in the second equation
c)
plug 4x+y in for y in the first equation
d)
set 2x+7 = 4x+y
23.
Solve each system of equations.
20x - 8y = 24
10x - 4y = 6
20x - 8y = 24
10x - 4y = 6
a)
No Solution
b)
Imop
c)
(1,1)
d)
(2,2)
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