Answer:
(x, y, z ) = (4, 8, 12 )
Explanation:
Given
x + y + z = 24 → (1)
5x + 3y + z = 56 → (2)
x + y - z = 0 → (3)
Eliminating z from the equations
Add (1) and (3) term by term
2x + 2y = 24 → (4)
Subtract (1) from (2) term by term
4x + 2y = 32 → (5)
Subtract (4) from (5) term by term
2x = 8 ( divide both sides by 2 )
x = 4
Substitute x = 4 into (4)
2(4) + 2y = 24
8 + 2y = 24 ( subtract 8 from both sides )
2y = 16 ( divide both sides by 2 )
y = 8
Substitute x = 4, y = 8 into (1)
4 + 8 + z = 24, that is
12 + z = 24 ( subtract 12 from both sides )
z = 12
Solution is x = 4, y = 8, z = 12