Chapter 8, Problem 26CR

To determine

To solve:

The given linear system of equations by graphing.

Answer to Problem 26CR

The solution for given system of equations would be $(3,-5)$ .

Explanation of Solution

Given:

A system of equations:

  $\begin{array}{l}2x+y=1\\ 4x-2y=22\end{array}$

Calculation:

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

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

  $\begin{array}{l}4x-2y=22\left(\text{Given equation}\right)\\ 4x-4x-2y=22-4x\left(\text{Subtracting 4}x\text{ from both sides}\right)\\ -2y=-4x+22\\ \frac{-2y}{-2}=\frac{-4x}{-2}+\frac{22}{-2}\left(\text{Dividing both sides by }-2\right)\\ y=2x-11\end{array}$

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 $(3,-5)$ . Therefore, the solution for given system of equations would be $(3,-5)$ .