Question

x+y+3z=12
-3x+7y-2z+=-35
7x-6y-5z=32

Answer 1

Interpret the second equation as -3x + 7y - 2z = -35. Solve by substitution:

From (1) x = 12 - y - 3z.

Substitute into (2) and (3):
(2) -> -3(12 - y - 3z) + 7y - 2z = -35 => 10y + 7z = 1
(3) -> 7(12 - y - 3z) - 6y - 5z = 32 => y + 2z = 4

From y + 2z = 4, y = 4 - 2z. Substitute into 10y + 7z = 1:
10(4 - 2z) + 7z = 1 => 40 - 13z = 1 => z = 3.

Then y = 4 - 2(3) = -2, and x = 12 - (-2) - 3(3) = 5.

Solution: x = 5, y = -2, z = 3.