Question

how do I solve a three equation problem using elimanation.
-5x+8y+3z=122
7x-2y-12z=-783
-8x-9y-10z=15 ?
I just want to know how to solve step by step -_-

Answer 1

You have 3 equations with 3 variables so that is the number one clue this can work.
You have two different ways to solve this: (1) is substitution and (2) is elimination.
If we were substituting you would take the first equation and set it to one variable-
Ex) x=(-783+12y+2y)/7, and then you'd "plug and chug"

However, you have already stated you can only use substitution so this can be even easier if you think about it.

Let's start with the first two equations:
-5x +8y+3z=122
7x-2y-12z=-783

Now you want to get rid of a variable so let's just get rid of "y" because then I only have to change one of the equations.

-5x +8y+3z=122
7x-2y-12z=-783
These are totally different equations and if we subtract them from each other we are still stuck with three different variables- NOT WHAT WE WANT SO, we multiply the second equation by 4 so that we can ELIMINATED "y":

-5x+8y+3z=122
4(7x-2y-12z=-783) --> 28x-8y-48z=-3132

Now we line them up and subtract:
-5x+8y+3z=122
28x-8y-48z=-3132
-----------------
23x -45z=-3010 (equ. 1)

Now you do the same with the other equation. Do you understand it or do you still need some help?