Chapter 16.3, Problem 4MRE

To determine

To evaluate: the real solution of the system.

Answer to Problem 4MRE

The solution of the given equations is $\left(-\frac{7}{5},\frac{34}{5}\right)$ .

Explanation of Solution

Given:

A system of equation is given as

  $\begin{array}{l}4m+2n=8\\ 3m-n=-11\end{array}$

Consider the system.

  $\begin{array}{l}4m+2n=8\mathrm{......}(1)\\ 3m-n=-11\mathrm{......}(2)\end{array}$

Substituting the value of ‘ n’ from equation (2) in equation (1).

  $\begin{array}{l}n=3m+11\\ 4m+2\left(3m+11\right)=8\\ 4m+6m+22=8\\ 10m=-14\\ m=-\frac{7}{5}\end{array}$

When $m=-\frac{7}{5}$ ,

  $\begin{array}{c}n=3m+11\\ =3\left(-\frac{7}{5}\right)+11\\ =-\frac{21}{5}+11\\ =\frac{34}{5}\end{array}$

So, the solution of the given equations is $\left(-\frac{7}{5},\frac{34}{5}\right)$ .