10x+4y + 12z=120

11x + 77y = 220

8x + 2y + 32z = 160

x=8.94; y = 1.58; z=2.02

Step-by-step explanation:

solve 10x+4y+12z = 120 → 5x+2y+6z = 60

8x + 2y + 32Z = 160 → 4x+y+16z = 80

To eliminate z multiply first equation by 16 and second equation by 6.

80x+32y+96z = 960

24x+6y+96z = 480

on subtractionwe get 56x+26y = 480

dividing by 2 we get, 28x + 13y = 240

Now we have a given equation 11x + 77y = 220 → x + 7y = 20

solving 28x + 13y = 240 and x + 7y = 20

28x + 13y = 240

28x + 216y = 560

subtracting we get, 203y = 320

y = 1.58

x = 8.94

z = 2.02