Solving Systems of Equations by Substitution Review

Solve the system of equations by using the Substitution Method.

y = 2x - 4

7x - 2y = 5

• (-1, -6)

• (-1, -8)

• (-2, 6)

• (1, -8),

Put the steps for solving by SUBSTITUTION in order:

• Solve one equation for x or y

• Solve for the first variable

• Solve for the second variable

• Plug that number into the other equation

• Plug the resulting expression into the other equation

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(​ (a)   )-2​ (b)   =-6

36-​ (c)   y-2y=​ (d)  

36-​ (e)   =-6

• 9-3y

• y

• 12

• -6

• 14y

• x

• 10y

• x+3y

• 24y

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(​9-3y)-2​y =-6

36-​12y-2y=​-6

36-​14y =-6

-14y=​ (a)  

y=​ (b)  

• -42

• 3

• 30

• -3

What is the solution to the system of equations?

4x-y=3

3x+y=4

(​ (a)   ,​ (b)   )

• 1

• 2

• 3

• 4

• 5

• 6

• 7

• 8

• 9

• 0

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​

In this system

x+3y=9

4x-2y=-6

we have figured out that x=9-3y, and y=3.

Complete the steps to solve for x:

x=9-3(​ (a)   )

x=9-​ (b)  

x=​ (c)  

The solution to the system is (​ (d)   ,​ (e)   ).

• 3

• 9

• 0

• y

• x

• y=3

• 3y

• -9

• 18

Consider the system

4x+3y=-1

5x+4y=1

After we do this multiplication, what will the new equations be?

​ 4(4x+3y=-1) ---> ​ (a)   x +​ (b)   y=​ (c)  

​-3(5x+4y=1)​ ---> ​ (d)   x -​ (e)   y= -3

• 16

• 12

• -4

• -15

• 3

• 5

• 1

• -1

• -12

• -3

Consider the system:

4x+3y=-1

5x+4y=1

Which we converted to:

16 x +​ 12y=​-4

-15x -​ 12y= -3

Combining the equations straight down gives us:

​ (a)   x+​ (b)   y=​ (c)  

Solving for x, we get x=​ (d)  

• 1

• 0

• -7

• 3

• 5

• -1

• -12

• -3

Consider the system:

4x+3y=-1

5x+4y=1

Since we now know that x=-7, solve for y:

4(​ (a)   )+3y=-1

​ (b)   +3y=-1

​ (c)   =​ (d)  

y=​ (e)  

• -7

• -28

• 3y

• 27

• 9

• 5

• 7

• -12

• 3

• y