Chapter 9.4, Problem 31WE

To determine

To find: The graph of the given two equations are coincide.

Answer to Problem 31WE

The graph of the given two equations are coincide is shown below.

Explanation of Solution

Given:

The give two equations are as:

  $\begin{array}{l}\frac{x-2y}{x+2y}=\frac{1}{3}\dots \left(1\right)\\ \frac{x-y}{x+y}=\frac{3}{5}\dots \left(2\right)\end{array}$

In order to show the graphs of the given equations are coincide, first, it is need tosimplified the given equations in terms of $x$ and $y$ .

So the simplified form of the equation $\left(1\right)$ is given as:

  $\begin{array}{c}\frac{x-2y}{x+2y}=\frac{1}{3}\\ 3\left(x-2y\right)=x+2y\\ 2x-8y=0\\ x=4y\end{array}$

Further, the simplified form of the equation $\left(2\right)$ is given as:

  $\begin{array}{c}\frac{x-y}{x+y}=\frac{3}{5}\\ 5\left(x-y\right)=3\left(x+y\right)\\ 2x-8y=0\\ x=4y\end{array}$

As the two given equations has the same slope $4$ and the same $y$ intercept $0$, so it is concluded that:

The graph of the given two equations are coincide.

The graph of the above given equations is given as:

  

Therefore, the graph of the given two equations are coincide is shown above.