X-y+5z=3

4x+z=0

x+3y+z=-9

x - y + 5z = 3 ... (1)

4x + z = 0 ... (2)

x + 3y + z = - 9 ... (3)

From (2) z = - 4x, Substitute for z in (1) and (3) : -

x - y + 5 (-4x) = 3

-19x + y = 3 ... (4)

x + 3y - 4x = - 9

-3x + 3y = - 9

- x + y = - 3 ... (5)

Subtract: - (4) - (5) we get

-18x = 0

x = 0

So z = - 4x = 0

Substituting for x and z in equation (3) : -

3y = - 9

y = - 3

Answer is x = 0, y = - 3 and z = 0