Answer:
w = 1
x = 4
y = 3
z = 2
Explanation:
Label the equations to communicate better
(1) w + y + z = 6
(2) 2w + x + z = 8
(3) 3w + x + y = 10
(4) x + y + z = 9
Subtract equation (1) from (2)
(2) 2w + x + z = 8
(1) w + y + z = 6
w + x - y = 2 (5)
Subtract equation (2) from (3)
(3) 3w + x + y = 10
(2) 2w + x + z = 8
w + y - z = 2 (6)
Add equations (5) and (6)
w + x - y = 2 (5)
w + y - z = 2 (6)
2w + x - z = 4 (7)
Subtract equation (7) from (2)
(2) 2w + x + z = 8
(8) 2w + x - z = 4
2z = 4
z = 2
Sub z=2 in (4)
x + y + z = 9 (4)
x + y + 2 = 9
x + y = 7 (8)
Sub (8) in (3)
3w + (x + y) = 10 (3)
3w + 7 = 10
3w = 3
w = 1
Sub w = 1 and z = 2 in (1)
w + y + z = 6 (1)
1 + y + 2 = 6
y + 3 = 6
y = 3
Sub y=3 and z=2 in (4)
x + y + z = 9 (4)
x + 3 + 2 = 9
x + 5 = 9
x = 4