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:

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

To make the first element in the second row a 0, divide the second row by 3 and then subtract row 1 from the resultant row 2

$\begin{array}{r}\left[\begin{array}{ccc}1& −1& 5\\ 3& 3& 3\end{array}\right]\stackrel{\frac{1}{3}{R}_2}{→}\left[\begin{array}{ccc}1& −1& 5\\ 1& 1& 1\end{array}\right]\\ \stackrel{R_2−R_1}{→}\left[\begin{array}{ccc}1& −1& 5\\ 0& 2& −4\end{array}\right]\end{array}$

To make the second element in the second row a 1, divide the second row by 2.

$\left[\begin{array}{ccc}1& −1& 5\\ 0& 2& −4\end{array}\right]\stackrel{\frac{1}{2}{R}_2}{→}\left[\begin{array}{ccc}1& −1& 5\\ 0& 1& −2\end{array}\right]$

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

$\left[\begin{array}{ccc}1& −1& 5\\ 0& 1& −2\end{array}\right]\stackrel{R_1+R_2}{→}\left[\begin{array}{ccc}1& 0& 3\\ 0& 1& −2\end{array}\right]$$\left[\begin{array}{ccc}1& −1& 5\\ 0& 1& −2\end{array}\right]\stackrel{R_1+R_2}{→}\left[\begin{array}{ccc}1& 0& 3\\ 0& 1& −2\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$(3,−2)$.