Which is the solution to the following system x+2y+z=9
X-y+3z=13
2z=10

2z = 10
/2 on both sides
z = 5
———————
x + 2y + z = 9
x + 2y + 5 = 9
-5 on both sides
x + 2y = 4
———————
x - y + 3z = 13
x - y + 3(5) = 13
x - y + 15 = 13
-15 on both sides
x - y = -2
———————
x + 2y = 4
x - y = -2

x + 2y = 4
- (x - y = -2)

x + 2y = 4
-x + y = 2
Add the equation together
3y = 6
/3 on both sides
y = 3
———————
Substitute z = 5 and y = 3 in one of the equations that includes all of the variables
x + 2y + z = 9
x + 2(3) + 5 = 9
x + 6 + 5 = 9
x + 11 = 9
-11 on both sides
x = -2
———————

Answers:
x = -2
y = 3
z = 5