Question

How do you solve the following system?: `x + 2y = 6 , 3x + 4 = -4y`

Answer 1

x = -16, y = 11

Explanation:

I’m going to be using elimination:

First isolate 4 by subtracting 3x from both sides:

`3x + 4 = -4y`
`-3x -4y =4`

Now I’m going to line the two equations up to see which variable I can cancel out first

`x+2y=6`
`-3x-4y=4`

I choose `y` because it seems to be the cleanest out of the two. Now multiply the first equation by 2 in order to cancel out `y` and then solve for `x`

`2(x+2y=6) = 2x+4y=12`

`2x+4y=12`
`+`
`-3x-4y=4`
———————
`-x=16`
`x=-16`

Time to solve for `y` by plugging in `-16` for `x` in either equation. It’s best to choose the equation that seems more efficient

`(-16) +2y=6`
`+16`

`{2y}/2 =22/2`

`y=11`