# Thread: Substitution & Elimination Methods

1. ## Substitution & Elimination Methods

Solve using substitution method:

x+y= -9
y= -2x + 3

Solve using elimination method:
-x+2y=12
2x-2y = 18

Thanks

2. Originally Posted by Suwanee
Solve using substitution method:

x+y= -9
y= -2x + 3
First solve one of your equations for one of the unknowns. It doesn't matter which in this case, but typically you want to solve the least complicated equation first. I will solve the top equation for "y" first:
y = -x - 9

Now insert this value of y into the second equation, then solve it for x.
(-x - 9) = -2x + 3
2x -x - 9 = 2x - 2x + 3
x - 9 = 3
x = 9 + 3 = 12.

Now insert this value for x into your solved y equation and that will give you the y value:
y = -(12) - 9 = -21.

So your solution is (x, y) = (12, -21).

-Dan

3. Originally Posted by Suwanee
Solve using elimination method:
-x+2y=12
2x-2y = 18
Here you want to "match" the coefficients of one of the variables, but you want one to be the negative of the other. To demonstrate, note that the coefficient of x in the top equation is -1 and the coefficient in the bottom equation is 2. Let's change the coefficient of the x in the top equation to -2 by multiplying both sides of the top equation by 2:

-2x + 4y = 24
2x - 2y = 18

Now we want to add the two equations together. We do this by adding the LHS of the top and bottom equations together, and adding the RHS of the top and bottom equations together. This gives:
4y - 2y = 24 + 18
2y = 42

y = 21.

Now "match" the y coefficients (in the original set of equations.) I'm going to do nothing, since they already "match." So add the original two equations together:
-x+2y=12
2x-2y = 18

Gives:
-x + 2x = 30
x = 30.

So your solution is (x, y) = (30, 21).

-Dan

4. ## Thanks topsquark

This helps a lot.

5. Originally Posted by Suwanee
This helps a lot.
No problemo!

-Dan