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# Solve the system of linear equations

4x+y-2z=0
2x-3y+3z=9
-6x-2y+z=0

### 1 Answer by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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4X + Y - 2z = 0
2X -3Y + 3Z = 9
-6X - 2Y + Z = 0

4X +Y - 2Z = 0         0X  + 7 Y - 8Z = -18        4X + Y - 2Z = 0           4X  + Y -2Z = 0
-2 ( 2X - 3Y + 3Z = 9)   3(2X - 3 Y + 3Z) = 9     4 ( 0X -11y +10Z = 27 )   0X - 9Y +0Z = 18
-6X  -2Y +Z = 0        -6X -2Y  + Z    =0       5 ( 0X  +7Y  -8Z  = -18)   0X +7Y -8Z  = -18

4X + Y - 2Z = 0        4X + Y -2Z = 0          4X +0 Y +0Z = 3
0X + Y + 0Z =-2       0X + Y+ 0Z =-2         0X + Y + 0Z  = -2
0X + 0Y - 8Z = -4     0X  + 0Y +Z = 1/2     0X  + 0Y + Z = 1/2

X = 3     Y = -2    Z = 1/2 are the answers:
Following procedure:
first eliminated X in both sides by multiplying 2nd equation by -2 and adding with first one
and 2nd equation by +3 and adding to 3rd one. The System reduces from 3 equation to 2 , and solve
then Y, and Z will be substituted to 1st equation and value of X will be calculated.