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:

$\left[\begin{array}{ccc}1& −2& −5\\ 2& 3& 4\end{array}\right]$

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

$\left[\begin{array}{cc}1& −2\text{|}\\ 2& 3\text{|}\end{array}\begin{array}{c}−5\\ 4\end{array}\right]\stackrel{R_2−2R_1}{→}\left[\begin{array}{cc}1& −2\text{|}\\ 0& 7\text{|}\end{array}\begin{array}{c}−5\\ 14\end{array}\right]$

To make the second element in the second row a 1, multiply the second row by$1/7$.

$\left[\begin{array}{cc}1& −2\text{|}\\ 0& 7\text{|}\end{array}\begin{array}{c}−5\\ 14\end{array}\right]\stackrel{\frac{1}{7}{R}_2}{→}\left[\begin{array}{cc}1& −2\text{|}\\ 0& \text{1|}\end{array}\begin{array}{c}−5\\ 2\end{array}\right]$

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

$\left[\begin{array}{cc}1& −2\text{|}\\ 0& \text{1|}\end{array}\begin{array}{c}−5\\ 2\end{array}\right]\stackrel{R_1−2R_2}{→}\left[\begin{array}{cc}1& 0\text{|}\\ 0& \text{1|}\end{array}\begin{array}{c}−1\\ 2\end{array}\right]$

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 localid="1647598364965">xis 0 and the coefficient of$y$is 1. Therefore, the solution is$(−1,2)$.