# help completing 4x - 6y = 12, 2x + 2y = 6

#### craze9321

##### New member
4x - 6y = 12
2x + 2y = 6

How do I complete this problem??? :?:

#### Mrspi

##### Senior Member

craze9321 said:
4x-6y=12
2x+2y=6

how do i complete this problem??? :?:
It would have been extremely helpful if you had indicated what methods you are using to solve systems....

Since you didn't, I'll show you ONE way (there are certainly others which would work!) that you might use.

Note that the coefficient of the y term in the first equation is -6. If we multiply both sides of the second equation by 3, the coefficient of the y term will be +6. If we then ADD the two equations together, we can eliminate the y term.

Here's the first equation:
4x - 6y = 12

Multiply both sides of the second equation by 3:
3(2x) + 3(2y) = 3(6)
or,
6x + 6y = 18

Now, use the first equation and the "new and improved" second equation:
4x - 6y = 12
6x + 6y = 18

ADD the two equations together:
4x - 6y = 12
6x + 6y = 18
---------------
10x + 0y = 30

or,
10x = 30

Divide both sides of this equation by 10, and you get
x = 3

Ok...now we know that x = 3

Substitute 3 for x in one of the original equations. I'll use this one:
2x + 2y = 6
2(3) + 2y = 6
6 + 2y = 6

Subtract 6 from both sides, and you get
2y = 0
Divide both sides by 2:
y = 0

Now, we have x = 3 and y = 0. Check. Are both of the original equations true when x = 3 and y = 0? If so, you know the solution is correct.

I hope this helps you.