Chapter SH, Problem 6.7.15EP

To determine

The solution for the given equations.

Answer to Problem 6.7.15EP

  $\left(1,-4\right)$

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{l}x+y=-3\\ 3x-10y=43\end{array}$

Calculation:

The augmented matrix can be written as:

  $=\left[\begin{array}{ccc}1& 1& -3\\ 3& -10& 43\end{array}\right]$

The solution can be obtained as:

  $\begin{array}{l}\left[\begin{array}{ccc}1& 1& -3\\ 3& -10& 43\end{array}\right]\stackrel{-3R_1+R_2}{\to }\left[\begin{array}{ccc}1& 1& -3\\ 0& -13& 52\end{array}\right]\stackrel{-\frac{1}{13}{R}_2}{\to }\left[\begin{array}{ccc}1& 1& -3\\ 0& 1& -4\end{array}\right]\\ \stackrel{-R_2+R_1}{\to }\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& -4\end{array}\right]\end{array}$

Hence, the solution is $\left(1,-4\right)$