1) x + y + z = 5
2) 2x + 4y + 2z = 6
3) -x + 6y - 3z = 21
add eq(1) and (3):
x + y + z = 5
-x + 6y - 3z = 21
_____________
7y - 2z = 26 (a)
multiply eq(3) by 2, add to eq(2):
2x + 4y + 2z = 6
-2x + 12y - 6z = 42
________________
16y - 4z = 48 (b)
multiply eq(a) by -2, add to eq(b);
-14y + 4z = -52
16y - 4z = 48
_______________
2y = -4
y = -4/2 = -2
using eq(b):
16(-2) - 4z = 48
-32 - 4z = 48
-4z = 80
z = 80/-4 = -20
using eq(1):
x + (-2) + (-20) = 5
x = 27
check using eq(2):
2(27) + 4(-2) + 2(-20) = 6
54 - 8 - 40 = 6
6 = 6
x = 27, y = -2, z = -20