Chapter 8, Problem 22CT

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 22CT

There areinfinitely many solutions for given system of equations.

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}3x-y=-7\\ -3x+y=7\end{array}$

Calculation:

First of all, we will convert our equations in slope-intercept form as shown below:

  $\begin{array}{l}3x-y=-7\left(\text{Given equation}\right)\\ 3x-3x-y=-7-3x\left(\text{Subtracting 3}x\text{ from both sides}\right)\\ -y=-3x-7\\ \frac{-y}{-1}=\frac{-3x}{-1}-\frac{7}{-1}\left(\text{Dividing both sides by }-1\right)\\ y=3x+7\end{array}$

  $\begin{array}{l}-3x+y=7\left(\text{Given equation}\right)\\ -3x+3x+y=7+3x\left(\text{Adding 3}x\text{ on both sides}\right)\\ y=3x+7\end{array}$

We can see that both equations represent same line.

Upon graphing both equations, we will get same line as shown below:

  

Upon looking at our graph, we can see that both lines intersect at infinitely many places. Therefore, there areinfinitely many solutions for given system of equations.