[alexaaa369]

How do you solve this by elimination?

-2x+4y=12
3x-2y=-10

please show step by step! Thank you!!

[jcaron2]

In order to solve a system of equations with elimination, you have to add or subtract the equations together to try to get one of the variables to cancel out.

Let's consider your two equations:

-2x+4y=12
3x-2y=-10

We could try adding them together as is. That means we add everything on the left side of each equation together, and we set it equal to the sum of everything on the right:

x + 2y = 2

Hmmm... That didn't accomplish anything. It resulted in another equation, and one which is perfectly valid, but you're no closer to solving for x and y.

Instead, we need to "scale" one of the equations (in other words, multiply or divide both sides by some value) so that it will cancel out one of the variables when you add the equations together. For example, let's say we want to cancel out the y terms, so the resultant equation is only a function of x. That way we can solve for x. Your original equations are

-2x+4y=12
3x-2y=-10

If we want the y terms to cancel, we need the coefficient of y in one equation to be exactly the negative of the coefficient in the other equation. Notice that the y-coefficient is 4 in the top equation, and it's -2 in the bottom one. So we could choose to multiply the bottom equation by 2 (so that it's y-coefficient becomes -4, exactly the negative of the y-coefficient of the top equation):


-2x+4y=12
2*(3x-2y)=2*(-10)

-2x+4y=12
6x-4y=-20

Now the y-coefficients are equal and opposite so if we add the two equations together, the y-terms cancel:

4x = -8

Which we can solve to find

x = -2

At this point, you have several options to solve for the other variable, y. You could start with the original two equations and go through a similar elimination process, only this time do it for x, so that you end up with an equation that's only got y terms. Much simpler than that, however, would be to simply plug x = -2 into either of your equations, and then solve for y.

For example, using the first equation:

-2x+4y=12
-2*(-2)+4y=12
4y = 8
y = 2

Or you just as easily could have chosen the second equation:

3x-2y = -10
3*(-2)-2y = -10
-2y = -4
y = 2

Notice you get the same answer either way. That's a good way to check that your answer is correct.

So there you have it. X = -2; y = 2

[alexaaa369]

Thank you so much!!

[jcaron2]

You're welcome. Hopefully that at least makes it a little bit clearer.