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

1 Answer

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.)