SOLUTION: solve the system x-y+2z=7 2x+z=4 x+5y+z=9

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Question 331613: solve the system x-y+2z=7
2x+z=4
x+5y+z=9

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
solve the system:
system%28x-y%2B2z=7%2C%0D%0A2x%2Bz=4%2C%0D%0Ax%2B5y%2Bz=9%29

Since y is already missing in the middle equation, we will
eliminate y from the other two equations:

system%28x-y%2B2z=7%2C%0D%0Ax%2B5y%2Bz=9%29

To make the y's cancel we multiply the first one through by 5

system%285x-5y%2B10z=35%2C%0D%0Ax%2B5y%2Bz=9%29

Adding corresponding terms causes the y's to cancel:

6x%2B11z=44

Now we put that with the original middle equation that
already had y eliminated:

system%286x%2B11z=44%2C%0D%0A2x%2Bz=4%29

To make the x's cancel we multiply the second one through by -3:

system%286x%2B11z=44%2C%0D%0A-6x-3z=-12%29

Adding corresponding terms causes the x's to cancel:

8z=32
z=4

Substitute that in 

2x%2Bz=4%29
2x%2B4=4
2x=0
x=0

Substitute that and z=4 in one of the original
three equations, that contains a y:

x-y%2B2z=7
%280%29-y%2B2%284%29=7
-y%2B8=7
-y=-1
y=1

So the solution is (x,y,z) = (0,1,4)

Edwin