Question

4x + 12 = -7y
-y + 12 = 4x
Solve with elimination

Answer 1

`\begin{cases}4x + 12 = -7y \\ -y + 12 = 4x \end{cases} \\ \\\begin{cases}4x + 7y = -12 \\ -4x-y =-12 \end{cases} \\+ ------- \\6y=-24\ \ /:6\\ \\y=-(24)/(6)\\ \\y=-4`


`4x+12=-7y\\ \\ 4x+12=-7*(-4)\\ \\4x=28-12\\ \\4x=16\ \ /:4\\ \\x=(16)/(4)\\ \\ x=4 \\ \\ \begin{cases}x=4 \\ y=-4 \end{cases}`

Answer 2

Take the second equation and flip it around so the y on the left ends up on the right and the 4x on the right ends up on the left. This makes all negatives positive and all positives negative. -4x + 12 = y

Then add the first equation to the second equation
4x +12 = -7y
-4x + 12 = y this eliminates the x's
24 = - 6y then divide by - 6
- 6 - 6
- 4 = y

So if you know that y = negative 4, you can substitute into either equation. I pick the second one because I am a lazy person.
-y + 12 = 4 x
-(-4) + 12 = 4 x combine your numbers
16 = 4 x then divide by 4
4 = x
So your solution is: x = 4 and y = -4 or this is also written (4, -4)

Does that work for you?