solve for x, y and z when

2x + 4y + 2z = 144
4x + y + 0.5z = 120
x + 3y + 4z = 144

1 answer

Multiply Eq2 by -4 and add Eq1 and Eq2:

2x + 4y + 2z = 144
-16x - 4y - 2z = -480
Sum: -14x = -336
X = 24

Multiply Eq1 by -2; add Eq1 and Eq3:
-4x - 8y - 4z = -288
+x + 3y + 4z = 144
Sum: -3x - 5y = -144.
X = 24. Solve for y:
-3*24 - 5y = -144
-72 - 5y = -144
-5y = -144 + 72 = -72
Y = 14.4

Eq1: 2x + 4y + 2z = 144
X = 24, Y = 14.4. Solve for Z.
2*24 + 4*14.4 + 2z = 144
48 + 57.6 + 2z = 144
2z = 144 - 48 - 57.6 = 38.4
Z = 19.2