Solve the system

Question

8x-y+2z=-21

x+2y-z=-1

2x+2y-3z=3

Answer 1

Eliminates y first....

multiplies first equation by 2 and adds to the second equation:

17x + 3z = -43

THen subtracts equation 3 MINUS equation 2:

x - 2z = 4

x = 4 +2z

17(4+2z) + 3z = -43

68 + 34z + 3z = -43

37z = -111

z = -3

then x = 4+2z = 4+2(-3) =4 + -6 = -2

x + 2y - z = -1

-2 + 2y - -3 = -1

-2 + 2y + 3 = -1

2y + 1 = -1

2y = -2

y = -1

x = -2, y = -1, z=-3