SOLUTION: x+2y+z=10 2x-y+3z=-5 2x-3y-5z=27 I need help on solving this when I put the 1st and 2nd equation together and multiply the 1st equation by -2 to eliminate the x's I get -5y+z=

Question 687929: x+2y+z=10
2x-y+3z=-5
2x-3y-5z=27
I need help on solving this when I put the 1st and 2nd equation together and multiply the 1st equation by -2 to eliminate the x's I get -5y+z=25. Then I put the 2nd and 3rd equation together mulitiply the 2nd equation by -1 to elimate the x's and I get -2-8z=32. I then put the 2 new equations together -5y+z=25 and -2y-8z=32 and multiply the first one by 8 to eliminate the z's. I am messing up somewhere and I'm not sure where. In my homework it is hit and miss I get some right and i get some wrong. Can you help me find my mistake?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x+2y+z=10
2x-y+3z=-5
2x-3y-5z=27
------
Subtract 2*1st row from 2nd
Subtract 2*1st row from 3rd
-------
x+2y+z=10
0x -5y +z = -25
0x -7y -7z = 7
-------
Multiply 2nd by 7
Multiply 3rd by 5
--------
x+2y+z=10
0x -35y + 7z = -175
0x -35y -35z = 35
-------
Subtract 2nd from 3rd to get:
------------------
x+2y+z=10
0x -15y +10z = -75
0x + 0y -42z = 210
-----------------------
Solve for "z":
z = -5
----
Substitute into 2nd and solve for "y"
y = 4
Substitute z and y into 1st and solve for "x"
x = 7
=================
cheers,
Stan H.

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