3x-y+2z=1
2x+3y+3z=4
x+y-4z=-9
You need to systematically eliminate one variable, say x, from the equations by subtracting a suitable multiple of one equation from all the others. Equation (3) begins with x so we'll use that.
3x-y+2z=1 ... (1)
2x+3y+3z=4 ... (2)
x+y-4z=-9 ... (3)
-4y + 14z = 28 ... (1)-3*(3) = (4)
y + 11z = 22 ... (2)-2*(3) = (5)
Now solve (4) and (5) for y and z and substitute the values for y and z into (3) to get x. Don't forget to check your answer!