Answer:
x=3
y=2
z=1
1 COMBINE ALL THREE EQUATIONS
x - y + x + z + y - z =1 + 4 + 1
2 RESHUFFLE
x + x - y + y + z - z = 6
3 SIMPLIFY
(cancel out the 'y's and 'z's, since there is a positive and a negative)
2x = 6
x = 6 ÷ 2
x = 3
4 REPLACE X WITH 3
3 - y = 1
-y = 1 - 3
-y = -2
y = 2
3 + z = 4
z = 4 - 1
z = 3
