The problem is an example of systems of linear equation with 3 variables. In order for us to get the solutions, we need to use Elimination. (1) Add the two equations to get z -x-2y+4z=-15 x+2y-5z=17 -------------------- -z = 2 z = -2
Then lets multiply 2x+y-z=7 by 2 --> 4x + 2y - 2z = 14
Then add it -x-2y+4z=-15 4x + 2y - 2z = 14 -x-2y+4z=-15 ----------------- -3x + 2z = -1
Substitute z to that equation -3x + 2(-2) = -1 -3x - 4 = -1 -3x = 3 x = 1
Then, using this equation 2x+y-z=7, substitute z and x 2(1) + y -(-2) = 7 2 + y +2 = 7 y = 7 -4 y = 3
