use elimination to solve the system of equations x-y+z=-1, x+y+3z=-3, 2x+y+2z=0

Question

you must use elimination to solve

Answer 1

Add eqns 1 and 2: 2x+4z=-4; divide through by 2: x+2z=-2.

Subtract eqn 2 from 3: x-z=3. Double this: 2x-2z=6 and add to eqn above: 3x=4, so x=4/3.

Therefore, z=x-3=4/3-3=-5/3. From eqn 2: 4/3+y-5=-3; y=-3+5-4/3=2/3.

The solution is x=4/3, y=2/3, z=-5/3.

Check the solution by substituting into the original equations to make sure they're true. All check out OK.