SOLUTION: solve through elimination, these things are killing me mentally! 5a-b+3c=5 2a+7b-2c=5 4a-5b-7c=-65

Question 219909: solve through elimination, these things are killing me mentally!
5a-b+3c=5
2a+7b-2c=5
4a-5b-7c=-65
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve through elimination, these things are killing me mentally!
5a-b+3c=5
2a+7b-2c=5
4a-5b-7c=-65
----------------------
Subtract the 3rd Eq. from the 1st to get:
1a+4b+10c=70
2a+7b-2c=5
4a-5b-7c=-65
----------------------
Subtract 2 times the 1st from the 2nd
Subtract 4 times the 1st from the 3rd
1a+4b+10c=70
0a-1b-22c=-135
0a-21b-47c=-345
----------------------------
Get rid of the negatives on the 2nd and on the 3rd Eqations:
1a+4b+10c=70
0a+1b+22c=+135
0a+21b+47c=+345
---------------------------
Subtract 21 times the 2nd from the 3rd to get:
1a+4b+10c=70
0a+1b+22c=135
0a+0b-415c=-2490
-----------------------
Divide thru the 3rd Eq. by -415 to solve for "c":
1a+4b+10c=70
0a+1b+22c=135
........c= 6
------------------------
Subtitute c=6 into the 2nd Eq to solve for "b"
1a+4b+10c=70
0a+1b+22*6=135
........c= 6
-----------------
c = 6
b = 3
substitute those into the 1st equation to solve for "a":
a + 4*3 + 10*6 = 70
a + 12 + 60 = 70
a+72 = 70
a = -2
=======================
Solution:
a = -2
b = 3
c = 6
================
Cheers,
Stan H.

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