X/2 +3y = 6 . . . . . . . . starting point
x/2 = 6 -3y . . . . . . . . subtract terms that don't have x
x = 2(6 -3y) . . . . . . . . multiply by the inverse of the x-coefficient
x = 12 -6y . . . . . . . . . expand if you like
3y = 6 -x/2 . . . . . . . . subtract terms that don't have y
y = (6 -x/2)/3 . . . . . . . multiply by the inverse of the y-coefficient
y = 2 -x/6 . . . . . . . . . expand if you like
First:
2x + 2z = 4
2(x+z)=4
x+z=4/2
x=2-z
-x - y - z= -8
-(2-z)-y-z= -8 replace x
-2+z-y-z= -8 (cancel z)
-2-y= -8
6 = y
Then:
-4x + 4y + 5z = 7 replace x and y
-4(2-z)+4*6 + 5z = 7
-8 + 4z + 24 + 5z = 7
16 + 9z = 7
9z = 7 - 16
9z = -9
z = -9/9
z= -1
Finally
x= 2-z replace z
x = 2- (-1)
x = 3
