Question

x-5y+3z=39
3x+8y-z=-19
2x-6y-5z=-29

Answer 1

Solve by substitution. From x - 5y + 3z = 39 we get x = 39 + 5y - 3z. Substitute into the other two:

3(39+5y-3z) + 8y - z = -19 → 23y - 10z = -136
2(39+5y-3z) - 6y - 5z = -29 → 4y - 11z = -107

Multiply the second by 10 and the first by 11 and subtract to eliminate z:
253y - 110z = -1496
40y - 110z = -1070
→ 213y = -426 → y = -2.

Then 4(-2) - 11z = -107 → -8 - 11z = -107 → z = 9.

Finally x = 39 + 5(-2) - 3(9) = 2.

Solution: x = 2, y = -2, z = 9. (You can verify these satisfy all three equations.)