x - 2y + 3z = 8 (eq. 1)
3y + z = 12 (eq. 2)
-2x + 2z = -4 (eq. 3)
Isolating x from equation 1:
x = 8 + 2y - 3z
Substituting this result into equation 3:
-2(8 + 2y - 3z) + 2z = -4
(-2)*8 + (-2)*2y + (-2)*(-3z) + 2z = -4
-16 - 4y + 6z + 2z = -4
-4y + 8z = -4 + 16
-4y + 8z = 12 (eq. 4)
Now, with equations 2 and 4 we have a system of 2 equations and 2 variables.
Isolating z from equation 2:
z = 12 - 3y
Substituting this result into equation 4:
-4y + 8(12 - 3y ) = 12
-4y + 8*12 - 8*3y = 12
-4y + 96 - 24y = 12
-28y = 12 - 96
-28y = -84
y = (-84)/(-28)
y = 3
Recalling the equation with z isolated:
z = 12 - 3(3)
z = 12 - 9
z = 3
Recalling the equation with x isolated:
x = 8 + 2(3) - 3(3)
x = 8 + 6 - 9
x = 5