`3x - 2y + z = -15, -x + y + 2z = -10, x - y - 4z = 14` Use matricies to solve the system of equations. Use Gaussian elimination with back-substitution.

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Multiply 2nd Row by 3 and add Row 1


Multiply 3rd Row by 3 and subtract it from Row 1


Subtract Row 2 from Row 3


Now the equations can be written as,

`3x-2y+z=-15`     ----equation 1

`y+7z=-45`          ------ equation 2

`6z=-12`                 ------ equation 3

From equation 3,


Now substitute back z in equation 2,





Substitute back the value of y and z in equation 1,







So the solution is x=-25, y=-31 and z=-2``


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