first equation:
x + y - z = 0
x + y = z
in the other 2 equations, replace z with x + y:
2x + 4y -(x+y) = 0
3x + 2y +2(x+y) = 0
simplify:
2x + 4y -x -y = 0
3x + 2y +2x +2y = 0
simplify more:
x + 3y = 0
5x + 4y = 0
in the top equation, move the 3y to the other side:
x = -3y
in the bottom equation, replace x with -3y:
5(-3y) + 4y = 0
-15y +4y = 0
-11y = 0
y = 0
but x = -3y, so:
x = -3(0)
x = 0
but x + y - z = 0, so:
0 + 0 - z = 0
z = 0
Answer: x = 0, y = 0, z = 0