91Ó°ÊÓ

To write the equations in augmented matrix place the coefficients of the equations and the constant terms into a matrix separated by a dashed line.

Here, the augmented matrices are:

$\left[\begin{array}{ccc}1& −2& |−26\\ 2& −3& |−42\end{array}\right]$

To make the first element in the second row a 0, multiply the first row by 2 and then subtract the resultant row 1 from the row 2.

$\left[\begin{array}{ccc}1& −2& |−26\\ 2& −3& |−42\end{array}\right]\stackrel{R_2→R_2−2R_1}{→}\left[\begin{array}{ccc}1& −2& |−26\\ 0& 1& |10\end{array}\right]$

Further row-reduce the augmented matrix, by making the second element in the first row a zero.

$\left[\begin{array}{ccc}1& −2& |−26\\ 0& 1& |10\end{array}\right]\stackrel{R_1→R_1+2R_2}{→}\left[\begin{array}{ccc}1& 0& |−6\\ 0& 1& |10\end{array}\right]$

Here, the first row will give the solution of $x$, because the coefficient of $y$ is 0 and the coefficient of $x$is 1. Similarly, the second row will give the solution of y, because the coefficient of $x$is 0 and the coefficient of $y$is 1. Therefore, the solution is $(−6,10)$.