SOLUTION: Three system of linear equation: x+3y-z=4 x+14y-5z=11 5x+19y-6z=13

Question 1016795: Three system of linear equation: x+3y-z=4
x+14y-5z=11
5x+19y-6z=13
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Three system of linear equation:
x+3y-z=4
x+14y-5z=11
5x+19y-6z=13
---------------
Subtract 1st row from 2nd
Subtract 5*1st row from 3rd
----------------------
x+3y-z=4
0x+11y-4z = 7
0x+4y-z = -7
---------------------
Multiply thru 2nd row by 4
Multiply thru 3rd row by 11
==================
x+3y-z = 4
0x+44y-16z = 28
0x+44y-11z = -77
---------------------------------
Subtract 2nd from 3rd row
----------
x+3y-z = 4
0x+44y-16z = 28
0x+0y+5z = -105
-------------------
Solve 3rd row for "z"::
z = -21
----
x+3y-z = 4
0x+44y-16z = 28
0x+0y+z = -21
----------
Multiply 3rd row by 16 and add to 2nd row::
x+3y-z = 4
0x+44y+0z = -308
0x+0y+z = -21
-----------
Divide thru 2nd by 44 to solve for "y"::
x+3y-z = 4
0x+y+0z = -7
0x+0y+z = -21
-----
Substitute and solve for x::
x = 4
------------
Cheers,
Stan H.
-----------

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