If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Systems of equations with substitution: 9x+3y=15 & y-x=5

Learn to solve the system of equations 9x + 3y = 15 and y - x = 5 using substitution. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• i am told to solve each system using substitution .
how would i do this problem ?

m=2n
m+4n=30
• brian,

Your first equation, m=2n, is already solved for m in terms of n, so plug that in your second equation like this:

m=2n, so
m+4n=30 is the same thing as (2n)+4n=30

Therefore 6n=30, so n= 5. And if n=5 and m=2n, m= 2(5) =10.

Rechecking:
m+4n=30. If m=10 and n=5
(10)+4(5)=30
10+20=30
30=30. The answer m=10 and n=5 checks good.

This method is called solving by substitution, because you first solve for one variable in terms of the other using 1 equation, and then you substitute that solution in the other equation to solve for the second variable explicitly. Then you go back and solve for the first variable explicitly.

Does that help?
• no one's asked a question in 5+1 years.
Why is that?
• i dont even know becuase you said this 4 years ago
• I have watched almost all the videos for substitution and I still do not understand. For example, for the system of equations x=2y+7, and x=y+4, I got x=-6 and y=-3, but I'm not sure I'm right.
Plug the y in to find x
x = y + 4 = -3 + 4 = 1

Then plug them both in the other equation to check
x = 2y + 7 = 2(-3) + 7 = -6 + 7 = 1
• is smth rong
• There are no errors at that time stamp. Why do you think something is wrong?
• How do I solve -8x + y= -3
3x + 2y =13
I can't seem to find something similar.
• This problem can be solved using substitution. It takes a few more steps than simpler ones, but here's how you do it:
The first equations seems simpler, since the y has a coefficient (number before the variable) of 1. If we add -8x to both sides of the equation, we get y = 8x - 3. Now we can substitute this in for y in the second equation to get: 3x + 2(8x-3) = 13, and then we just solve for x. If you did the steps right, you should get x= 1. Then, by putting in 1 for x in any of the two equations, you should get y=5.
Let's check our work. -8(1)+(5) = -8+5 = -3, and 3(1)+2(5) = 3 + 10 = 13. This is right, so our solution set is x=1, y=5, or (1,5).
• how do i solve
y=x-6
y=2x-8
via substitution
• Since y = x-6 and y = 2x-8, set x-6 equal to 2x-8.
x-6 = 2x-8
-6 = x-8 Subtract x from both sides.
x = 2 Add 8 to both sides.

Plug in x for 2 into the first equation y = x-6: y = 2-6 = -4
Verify that the second equation y = 2x-8 holds true: y = 2(2)-8 = -4, -4 = -4!
• How do you solve this equation -3x-8y= 20 -5x + y=19