Question

How do you solve using gaussian elimination or gauss-jordan elimination, `10x-20y=-14`, `x +y = 1`?

Answer 1

`x=1/5` and `y=4/5`

Explanation:

From the given , take note of the numerical coefficients of `x` and `y` and the constants.

the given

`10x-20y=-14`
`x+y=1`

Arrange in rows. So that first row for the first equation, second row for the second. First column for the coefficients of x, second column for the coefficients of y aand third column for the constants.

`X.......Y.........K`

`10 \ \ -20 \ \ ] \ \ -14`
`01 \ \ +01 \ \ ] \ \ +01`
~~~~~~~~~~~~~~~~~~

`01 \ \ -02 \ \ ]\ -7/5` ........this is after dividing row 1 by 10
`01 \ \ +01 \ \ ] \ \ +01`
~~~~~~~~~~~~~~~~~~

`01 \ \ -02 \ \ ]\ -7/5`
`\ \ 0 \ \ +03 \ \ ] \ +12/5` .........this is after changing the sign of
~~~~~~~~~~~~~~~~~~~~~ previous row 1 and adding result to row 2

`01 \ \ -02 \ \ ]\ -7/5`
`\ \ 0 \ \ +01 \ \ ]\ +4/5` .......this is after dividing previous row 2 by 3
~~~~~~~~~~~~~~~~~~
`\ 01 \ \ +0 \ \ ]\ +1/5`........this is after multiplying previous row 2
`\ \ 0 \ \ +01 \ \ ]\ +4/5` `\ \ ` `\ \ ` by 2 then adding result to row 1.

Take note of the coefficients at this point
`1*x+0*y=1/5`
`0*x+1*y=4/5`

The result `x=1/5`
and also `y=4/5`

Have a nice day !!! from the Philippines.