4x + 7y - 2z = 0
3x - 5y + 3z = 9
3x + 6y -z = 1
first try to eliminate z
multiply (-2) to this equation 3x + 6y -z = 1
-6x - 12y + 2z = -2
4x + 7y - 2z = 0
--------------------add
-2x - 5y = -2
Again, multiply (3) to this equation 3x + 6y -z = 1
9x + 18y -3z = 3
3x - 5y + 3z = 9
--------------------------add
12x + 13y = 12
Now you have 2 system equations w/o z
12x + 13y = 12
-2x - 5y = -2
Multiply (6) to this equation -2x - 5y = -2
-12x - 30y = -12
12x + 13y = 12
-------------------------add
43y = 0
y = 0
-2x - 5y = -2
-2x - 5(0) = -2
-2x = -2
x = 1
3x + 6y -z = 1
3(1) + 6(0) -z = 1
3 -z = 1
z = 2
Now you have x =1, y =0, z = 2
double check
4x + 7y - 2z = 0
4(1) + 7(0) - 2(2) =0
4 + 0 - 4 = 0
0 = 0
answer:
(1,0,2) last choice