10x+y+4z=1 X-2y-7z=-3 2x+y+5z=0

Solve the system:

1. 10x + y + 4z = 1
2. x - 2y - 7z = -3
3. 2x + y + 5z = 0

From (3): y = -2x - 5z.

Plug into (1): 10x + (-2x - 5z) + 4z = 1 => 8x - z = 1 => z = 8x - 1.

Plug y into (2): x - 2(-2x - 5z) - 7z = -3 => x + 4x + 10z - 7z = -3 => 5x + 3z = -3.

Substitute z = 8x - 1: 5x + 3(8x - 1) = -3 => 5x + 24x - 3 = -3 => 29x = 0 => x = 0.

Then z = 8(0) - 1 = -1 and y = -2(0) - 5(-1) = 5.

Solution: x = 0, y = 5, z = -1.

Quick check:

• (1): 0 + 5 + 4(-1) = 1 ✔
• (2): 0 - 10 - 7(-1) = -3 ✔
• (3): 0 + 5 + 5(-1) = 0 ✔