Question

How do you solve this system of equations: `12y - 5z = 19 and 12y + 16z = 40`?

Answer 1

Cancel some variable out to begin to solve.

Explanation:

First make one of the variables cancel out (I used y because it was easier)

`12y-5z=19`
`12y+16z=40`
Then make the 12's cancel out by multiplying any of them by a negative one (I did the bottom)
`12y-5z=19`
`-12y-16z=-40`
`-21z=-21`
`z=1`
Plug it back into any of the original formulas (I did the first)
`12y-5(1)=19`; `12y-5=19`; `12y=24`; `y=2`
Check it (both of them!)
`12(2)+16(1)=40`; `40=40`
`12(2)-5(1)=19`; `19=19`

There is other methods like substitution and matrix forms you can also do. (If you want those calculations, you can ask in a comment.)