First, eliminate one variable: by adding two equations:
10x+7y-2z=46 (a)
3x-2y+9z=22 (b)
5x+y-3z=28 (c)
Multiply (c) by 2 and subtract it to (a):
10x+7y-2z= 46
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10x+2y-6z=56
____________
5y+4z= -10 (1)
Add another 2:
Multiply (c) by 3 and subtract it to (b) multiplied by 5
15x-10y+45z= 110
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15x+3y-9z= 84
____________
-13y+36z= 26 (2)
Solve the system:
5y+4z= -10 (1)
-13y+36z= 26 (2)
Multiply (1) by 9 and subtract (2) to (1)
45y+36z= -90
-
-13y+36z=26
______________
58y=-116
y= -116/58
y= -2
Replace y on (1)
5(-2)+4z=-10
-10+4z=-10
4z=-10+10
4z=0
z=0
Replace z and y on a, b or c: and solve for x
10x+7y-2z=46 (a)
10x+7(-2)-2(0)= 46
10x-14=46
10x=46+14
10x= 60
x= 60/10
x= 6
solution:
x=6, y=-2 , z=0