Chapter 8, Problem 23CT

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 23CT

The solution for given system of equations would be $(0,-5)$ .

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}2x-y=5\\ x+2y=-10\end{array}$

Calculation:

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

  $\begin{array}{l}2x-y=5\left(\text{Given equation}\right)\\ 2x-2x-y=5-2x\left(\text{Subtracting 2}x\text{ from both sides}\right)\\ -y=-2x+5\\ \frac{-y}{-1}=\frac{-2x}{-1}+\frac{5}{-1}\left(\text{Dividing both sides by }-1\right)\\ y=2x-5\end{array}$

  $\begin{array}{l}x+2y=-10\left(\text{Given equation}\right)\\ x-x+2y=-10-x\left(\text{Subtracting }x\text{ from both sides}\right)\\ 2y=-x-10\\ \frac{2y}{2}=\frac{-x}{2}-\frac{10}{2}\\ y=-\frac{1}{2}x-5\end{array}$

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 $(0,-5)$ . Therefore, the solution for given system of equations would be $(0,-5)$ .