How do you solve using elimination of 2x - 3y = 12 and 3x + 5y = -1?

1 Answer
Jun 11, 2018

x=3
y=-2

Explanation:

On paper you should line the equations up, one below the other:

2x-3y=12
3x+5y=-1

In elimination, you have to find the least common multiple between one of the variables. I prefer to eliminate x and solve for y first and so the least common multiple between 2x and 3x is 6x.

You’ll have to multiply 2x-3y=12 by 3 and
3x+5y=-1 by 2

6x-9y=-36
6x+10y=-2

Now you have to combine the equations by subtracting the bottom equation from the top:

-19y=38
Notice that we added 2 to 36 because if you try to subtract a negative, the negative turns positive.

Now to isolate y, divide both sides by -19

y=-2

Now that we found y, let’s subtitute it into either equation to find x. I’ll choose the top equation:

2x-3(-2)=12
2x+6=12

Now, we subtract 6 from both sides in an attempt to isolate x.

2x=6

Divide both sides by 2

x=3

And there you go!

y=-2 and x=3

Hope this helps!