Solution
We have the following system of equations:
x-6y +4z= -12 (1)
x +y -4z = 12 (2)
2x +2y +5z = -15 (3)
We can subtract equation (1) from equation (2) and we got:
x-x + y+6y -4z-4z = 12+12
7y -8z = 24
and we can multiple the first equation by -2 and add to the (3) equation and we got:
2x -2x + 2y +12y +5z- 8z = 24-15
14y -3z = 9
Then solving for z we can do this:
14y -3z = 9
-14y + 16 z = -48
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13z = -39
z= -3
And solving for y we got:
7y = 24 +8(-3)= 24-24 = 0
y= 0
And solving for x from equation (1) we got:
x = 6y -4z -12 = 0 +12 -12= 0
Then the final solution is:
x= 0, y= 0, z= -3
