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:

$\left[\begin{array}{ccc}1& −2& −16\\ 3& 4& 72\end{array}\right]$

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

$\left[\begin{array}{ccc}1& −2& −16\\ 3& 4& 72\end{array}\right]\stackrel{R_2→R_2−3R_1}{→}\left[\begin{array}{ccc}1& −2& −16\\ 0& 10& 120\end{array}\right]$

To make the second element in the second row a 1, divide the second row by 10.

$\left[\begin{array}{ccc}1& −2& −16\\ 0& 10& 120\end{array}\right]\stackrel{\frac{1}{10}{R}_2}{→}\left[\begin{array}{ccc}1& −2& −16\\ 0& 1& 12\end{array}\right]$

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

$\left[\begin{array}{ccc}1& −2& −16\\ 0& 1& 12\end{array}\right]\stackrel{R_1→R_1+2R_2}{→}\left[\begin{array}{ccc}1& 0& 8\\ 0& 1& 12\end{array}\right]$

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 $\left(8,12\right)$.