Chapter 9.2, Problem 10WE

To determine

To find: Thesolution of the given equations by using substitution method.

Answer to Problem 10WE

The solution of the given equations by using substitution method is $m=2\text{and }n=-1$ .

Explanation of Solution

Given information:

The given equationsare,

  $\begin{array}{l}3n+5m=7\\ m-4n=6\end{array}$

The given equation can be writtenas,

  $\begin{array}{l}m-4n=6\\ m=6+4n\end{array}$

The another given equation is,

  $3n+5m=7$

Substitute $6+4n$ for $m$ .

  $\begin{array}{l}3n+5\left(6+4n\right)=7\\ 3n+30+20n=7\\ 23n=-23\\ n=-1\end{array}$

The value of $m$ is calculated as,

  $\begin{array}{c}m=6+4n\\ =6+4\left(-1\right)\\ =2\end{array}$

Thus, the solution of the given equations by using substitution method is $m=2\text{and }n=-1$ .