Label the equations:
(1) 2x+3y+2z=4
(2) 3x+4y+5z=-5
3x+6y+3z=-12⇒(3) x+2y+z=-4, after dividing through by 3.
2×(3)-(1): y=-8-4=-12, so y=-12 and we can create new equations by substituting y=-12 in the equations:
2x-36+2z=4⇒2x+2z=40⇒(4) x+z=20, after dividing through by 2.
(2) becomes 3x-48+5z=-5⇒(5) 3x+5z=43.
We don’t need any more equations because we now have two equations and two unknowns.
3×(4)-(5): -2z=60-43=17, so z=-17/2 and x=20-z=20+17/2=57/2.
SOLUTION: x=57/2, y=-12, z=-17/2.