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Worksheets

Solving Systems w Substitution

Total questions: 18

Worksheet time: 1hrs 19mins

Name
Class
Date
1.

Solve the following systems of equations using substitution:


y = 3 - x

3y + x = 5

a)

No solution

b)

(1, 2)

c)

(3, 0)

d)

(2, 1)

2.
Solve:
y=8x+1
y=6x+3
a)
(1, 9)
b)
(4, 14)
c)
(0, 1)
d)
(2, 4)
3.
What is the solution to this system?
2x + 3y = 4
y= 5x - 27
a)
(5,-2)
b)
(5, 2)
c)
(2,3)
d)
(3,2)
4.

Solve this system using substitution

y = 3x - 5

2x + 4y = -6

a)

(1, -2)

b)

(2, -2)

c)

(1, 2)

d)

Why have you done this?

5.
Solve each system using substitution:
y = 4x - 3
y = 2x + 13
a)
( 8 , 29)
b)
( 7 , 28)
c)
( - 1, -4)
d)
(3, 0)
6.
What is the solution of the graph.
a)
One Solution ( 1,2)
b)
One Solution (-1,0)
c)
No Solution
d)
Infinitely Many Solutions
7.

Solve the following systems of equations using substitution:


2y + x = -15

x = 3y

a)

(-3, -9)

b)

(-9, -3)

c)

(-3, 9)

d)

(9, -3)

8.

Find the solution of the system of equations below using the substitution method:


y = 2x - 4


7x - 2y = 5

a)

(-1, -6)

b)

(-1, -8)

c)

(-2, 6)

d)

(1, -8),

9.
a)

No Solution

b)

(2, 2)

c)

(-1, 2)

d)

(-1, -2)

10.

Solve systems by substitution.

4x + y = 49

y = 3x

a)

(-7,21)

b)

(7,-21)

c)

(7,21)

d)

(-7,-21)

11.
What is the first step in solving a system by Substitution?
a)
Make sure both equations are in standard form.
b)
Make sure at least one equation is solved for one variable.
c)
Make sure both equations are in slope-intercept form.
d)
Make sure both equations can be solved.
12.

How many solutions does the graph have?

a)

One solution

b)

No solution

c)

Infinite solutions

13.

How many solutions does the graph have?

a)

One solution

b)

No solution

c)

Infinite solutions

14.
What does
"solution to a system of equations"
mean?
a)
It's the point where both equations equal zero
b)
It's the point where graphs of both equations cross the y-axis
c)
It's the point that solves both equations at the same time
d)
It's the point where graphs of both equations cross the x-axis
15.

Give the solution to the system
a)
(3,1)
b)
(1,3)
c)
(-1,3)
d)
a hoppy hippo
16.

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

a)

The variable is already isolated, so we've already solved the system.

b)

The variable is already isolated for y, so we substitute it in the first equation and solve for x

3x + 3(3x + 5) = 3

c)

Free sha vaca doo

d)

The variable is already isolated for y, so we substitute it in the second equation and solve for x

y = 3(3x + 3y) = 3

17.
The first step in solving using the substitution method is __________.
a)
get x by itself
b)
get y by itself
c)
get either variable by itself
d)
add the equations together
18.
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