Solve the system of equations by finding x,y,z: x+y+z=-6, 2x+5y+2z=-30, -x+9y-3z=-66

Solve the system of equations by finding x,y,z:  x+y+z=-6   2x+5y+2z=-30   -x+9y-3z=-66

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Given x+y+z=-6.......(1)
2x+5y+2z=-30.........(2)
-x+9y-3z=-66........(3)

Multiply by -2 in equation(1) and add equation(2)
-2x-2y-2z=12......(1)
2x+5y+2z=-30.....(2)
..............
3y=-18
y=-6

Multiply by 3 in equation(1) and add equation(3)
3x+3y+3z=-18.....(1)
-x+9y-3z=-30.....(2)
............
2x+12y=-48.....(4)

Substitute y value in equation (4)
x=-6

Substitute x and y value in equation (1)
-6-6+z=-6
z=6

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