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:

$\left[\begin{array}{ccc}2& 3& 8\\ 1& −5& −22\end{array}\right]$

First exchange row 1 with row 2 so as to make the first element of row 1 a 1.

$\left[\begin{array}{ccc}2& 3& 8\\ 1& −5& −22\end{array}\right]\stackrel{R_1↔R_2}{→}\left[\begin{array}{ccc}1& −5& −22\\ 2& 3& 8\end{array}\right]$

To make first element of row to a 0, multiply row 1 by 2 and subtract the resultant from row 1.

$\left[\begin{array}{ccc}1& −5& −22\\ 2& 3& 8\end{array}\right]\stackrel{R_2−2R_1}{→}\left[\begin{array}{ccc}1& −5& −22\\ 0& 13& 52\end{array}\right]$

To make the second element in the second row a 1, divide the second row by 13.

$\left[\begin{array}{ccc}1& −5& −22\\ 0& 13& 52\end{array}\right]\stackrel{\frac{1}{13}{R}_2}{→}\left[\begin{array}{ccc}1& −5& −22\\ 0& 1& 4\end{array}\right]$

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

$\left[\begin{array}{ccc}1& −5& −22\\ 0& 1& 4\end{array}\right]\stackrel{R_1→R_1+5R_2}{→}\left[\begin{array}{ccc}1& 0& −2\\ 0& 1& 4\end{array}\right]$

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$(−2,4)$.