Solve by using the substitution method.

Question

x - 4y = 4

-2x - 5y = -21

 

Answer 1

Using the first equation, isolate x. This gives you x = 4 + 4y.

Plug x = 4 + 4y into the second equation as follows: -2(4 + 4y) - 5y = -21. (This step is the substitution step because you are replacing x with 4 + 4y).

 

Distribute: -8 - 8y - 5y = -21

Simplify: - 8 - 13y = -21

Bring to one side to solve for y: -13y = -13; y = 1.

 

Now plug y = 1 into the first or second equation to solve for x. I will plug it into the first equation because it's easier!

x - 4(1) = 4

x - 4 = 4

x = 8

 

Now I will plug in x = 8 and y = 1 into both equations to see if I obtain the answers I should.

Using the first equation:

8 - 4 = 4; yes!

-2(8) - 5(1) = -16 - 5 = -21; yes!