Question

solve the system of equations, x+3z=12, -x-2y+z=10, 3x+5y+2z=-7

Answer 1

x+3z=12 ------ (1)
-x-2y+z=10 ----- (2)
3x+5y+2z=-7 ------ (3)

First pick a variable to eliminate.
Let us eliminate x.
Add equations (1) and (2). That will eliminate x and you will have one equation with just y and z. Call this equation (4)
Multiply (1) by -3 and add it to (3). That That will eliminate x and you will have a second equation with just y and z. Call this equation (5)

Solve for y and z from (4) and (5). Then solve for x.