Chapter 6.3, Problem 2CB

To determine

To calculate:Thesolution of pair of two variable equations $-4x-4y=16\text{ \& }4x+5y=14$ using augmented matrix

Answer to Problem 2CB

The values of x and y is:

  $\begin{array}{l}x=-34\\ y=30\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}-4x-4y=16\\ 4x+5y=14\end{array}$

Calculation:

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

  $\left[\begin{array}{cc}-4& -4\\ 4& 5\end{array}|\begin{array}{c}16\\ 14\end{array}\right]$

Using matrix operation:

  $\begin{array}{l}{R}_1\to -\frac{1}{4}{R}_1\\ \left[\begin{array}{cc}1& 1\\ 4& 5\end{array}|\begin{array}{c}-4\\ 14\end{array}\right]\\ R_2\to R_2-4R_1\\ \left[\begin{array}{cc}1& 1\\ 0& 1\end{array}|\begin{array}{c}-4\\ 30\end{array}\right]\\ R_1\to R_1-R_2\\ \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}|\begin{array}{c}-34\\ 30\end{array}\right]\end{array}$

Hence, the values of x and y is:

  $\begin{array}{l}x=-34\\ y=30\end{array}$