Question

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

Answer 1

`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!