Question

In the form of the matrice, how do you work out the following simultaneous equation?
x+3y+7=0
x+y+1=0

Answer 1

$\left[\begin{array}{ccc}1&3&7\\1&1&1\end{array}\right]$
multiply 2nd row by -1 and add to first row
$\left[\begin{array}{ccc}0&2&6\\1&1&1\end{array}\right]$
divide the 1st row by 2
$\left[\begin{array}{ccc}0&1&3\\1&1&1\end{array}\right]$
multiply the first row by -1 and add to 2nd row
$\left[\begin{array}{ccc}0&1&3\\1&0&-2\end{array}\right]$

now we know
y+3=0
x-2=0

therefor
y=-3
x=2