Chapter 8.8, Problem 2C

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 2C

The given system of equations has infinitely many solutions.

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}x-y=-3\\ -4x+4y=12\end{array}$

Calculation:

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

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

  $\begin{array}{l}-4x+4y=12\left(\text{Given equation}\right)\\ -4x+4x+4y=12+4x\left(\text{Adding 4}x\text{ on both sides}\right)\\ 4y=12+4x\\ y=x+3\left(\text{Dividing both sides by }4\right)\end{array}$

We can see that both equations are same, so we will get same graph for both equationsas shown below:

  

Since the graphs have infinitely many points of intersection,therefore, the given system of equationshas infinitely many solutions.