Chapter 9.4, Problem 23WE

To determine

To find: The value of $n$ and $m$ by solving the given two linear equation.

Answer to Problem 23WE

Thevalue of $n$ is $2$ and the value of $m$ is $0$ .

Explanation of Solution

Given:

The given equations are:

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

To solve the given equations by substitution method, first, express the equation $\left(2\right)$ , as $n$ in terms of $m$ and then substitute the value of $n$ in equation $\left(1\right)$ So, the equation $\left(2\right)$ as $n$ in terms of $m$ is given as:

  $n=2-6m\dots \left(3\right)$

After substituting the above value of $n$ in equation $\left(1\right)$ , the calculation is as given:

  $\begin{array}{c}\frac{1}{2}\left(2-6m\right)-m=1\\ 1-3m-m=1\\ -4m=0\\ m=0\end{array}$

Further simplified, after substituting the value of $m=0$ in the equation $\left(3\right)$ , is as:

  $\begin{array}{c}n=2-6\left(0\right)\\ =2\end{array}$

Therefore, the value of $n$ is $2$ and the value of $m$ is $0$ .