Chapter 6.3, Problem 3CB

To determine

To calculate:The solution of pair of two variable equations $2x+2y=14\text{ \& }-x-2y=-13$ using augmented matrix

Answer to Problem 3CB

The values of x and y is:

  $\begin{array}{l}x=1\\ y=6\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}2x+2y=14\\ -x-2y=-13\end{array}$

Calculation:

The augmented matrix of the pair of two variable equations is:

  $\left[\begin{array}{cc}2& 2\\ -1& -2\end{array}|\begin{array}{c}14\\ -13\end{array}\right]$

Using matrix operation:

  $\begin{array}{l}{R}_1\to \frac{1}{2}{R}_1\\ \left[\begin{array}{cc}1& 1\\ -1& -2\end{array}|\begin{array}{c}7\\ -13\end{array}\right]\\ R_2\to R_2+R_1\\ \left[\begin{array}{cc}1& 1\\ 0& -1\end{array}|\begin{array}{c}7\\ -6\end{array}\right]\\ R_2\to -R_2\\ \left[\begin{array}{cc}1& 1\\ 0& 1\end{array}|\begin{array}{c}7\\ 6\end{array}\right]\\ R_1\to R_1-R_2\\ \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}|\begin{array}{c}1\\ 6\end{array}\right]\end{array}$

Hence, the values of x and y is:

  $\begin{array}{l}x=1\\ y=6\end{array}$