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

$x = \frac{1}{5}$ and $y = \frac{4}{5}$

#### Explanation:

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

the given

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

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.

$X \ldots \ldots . Y \ldots \ldots \ldots K$

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 $\setminus \setminus$ $\setminus \setminus$ by 2 then adding result to row 1.

Take note of the coefficients at this point
$1 \cdot x + 0 \cdot y = \frac{1}{5}$
$0 \cdot x + 1 \cdot y = \frac{4}{5}$

The result $x = \frac{1}{5}$
and also $y = \frac{4}{5}$

Have a nice day !!! from the Philippines.