What is the solution to this system of equations? x+3y-z=64x-2y+2z=-106x+z=-12

43x + 5y - 4z = 12

Step-by-step explanation:

x+3y-z=64x-2y+2z=-106x+z=-12

The solution is given if you group all x y and z together. The 'problem' is you have three equal signs ...

If you want, you can split it into three steps.

1. Group the two first equations.

x+3y-z=64x-2y+2z

x+3y-z=64x-2y+2z

x - 64x + 3y + 2y - z - 2z

-63x + 5y - 3z

2. Group the last two equations.

-106x+z=-12

-106x+z + 12 = 0

3. Now use answer 1. and set it equal to answer 2, and group these equations.

-63x + 5y - 3z = - 106x + z + 12

-63x + 106x + 5y - 3z - z = 12

43x + 5y - 4z = 12

And this is the answer we are looking for.