Question

Determine the intersection of the three planes with the following system of equations:
x - y + 2z = 0
3x + 2y - z= -5
4x + 2y - 2z = -6

Answer 1

multiply the second equation by 2 to get rid of z
x - y + 2z = 0
6x + 4y -2z= -10
4x + 2y - 2z = -6
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7 x + 3 y = -10
2 x + 2 y = - 4
multiply first by 2 and second by 3
14 x + 6 y = - 20
6 x + 6 y = -12
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8 x = - 8
x = -1
now go back up and get y and z

Answer 2

thanks