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Hi,
6x-3y-z= -19 
2x-2y+z= -15
8x-5y = -34
3x-y-z= -6
2x-2y+z= -15
5x - 3y = -21
8x-5y = -34
5x - 3y = -21 ||Multiply 1st by 3, 2nd by 5 and subtracting 1st from 2nd to eliminate y
x = -3 and y = 2 and z = -5