Chapter 8.8, Problem 4E

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 4E

The solution for given system of equations would be $(-1,4)$ .

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}x+y=3\\ x-y=-5\end{array}$

Calculation:

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

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

  $\begin{array}{l}x-y=-5\left(\text{Given equation}\right)\\ x-x-y=-5-x\left(\text{Subtracting }x\text{ from both sides}\right)\\ -y=-x-5\\ y=x+5\left(\text{Dividing both sides by }-1\right)\end{array}$

Upon graphing both equations, we will get our required graph as shown below:

  

Upon looking at our graph, we can see that both lines intersect at point $(-1,4)$ . Therefore, the solution for given system of equations would be $(-1,4)$ .