SOLUTION: Solve the system x-3y-z=7 2x+y-2z=0 x-y+z=1

Question 475967: Solve the system
x-3y-z=7
2x+y-2z=0
x-y+z=1
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
x-3y-z=7...............(1)
2x+y-2z=0.............(2)
x-y+z=1.................(3)
Add (1) and (3)
x-3y-z=7
x-y+z=1
--------------
2x-4y=8
2(x-2y)=8
x-2y=8/2
x-2y=4...............(4)
Now
Multiply (3) by 2 and add to (2)
2x-2y+2z=2
2x+y-2z=0
-------------
4x-y=2............(5)
Multiply (5) by -2 and substract from (4)
x-2y=4
-8x+2y=-4
-------------
-7x=0
-7x/-7=0/-7
X=0
Put value of x in (4)
0-2y=4
-2y=4
-2y/-2=4/-2
Y=-2
Put values of x and y in any of three equations (1),(2) or (3)
Lets put in (1)
x-3y-z=7...............(1)
0-3(-2)-z=7
6-z=7
-z=7-6
-z=1
z=-1
(x,y,z)=(0,-2,-1)
Check:
x-3y-z=7...............(1)
0-3(-2)-(-1)=7
0+6+1=7
7=7
2x+y-2z=0.............(2)
2(0)+(-2)-2(-1)=0
0-2+2=0
0=0
x-y+z=1.................(3)
0-(-2)+(-1)=1
0+2-1=1
1=1
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