Chapter 6.1, Problem 16PPE

To determine

To solve: the given system and then to verify the solution.

Answer to Problem 16PPE

The solution of system of equations is $(-4,4)$ .

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y=-\frac{1}{2}x+2\\ y=\frac{1}{2}x+6\end{array}$

Find the intercepts and draw the lines.

  $\begin{array}{l}y=-\frac{1}{2}x+2\\ y=0\Rightarrow x=4\\ x=0\Rightarrow y=2\\ y=\frac{1}{2}x+6\\ y=0\Rightarrow x=-12\\ x=0\Rightarrow y=6\end{array}$

Graph:

The graph of given system of equations is shown below.

The solution of system is $(-4,4)$ .

Verify the solution

  $\begin{array}{l}y=-\frac{1}{2}x+2\\ 4=-\frac{1}{2}(-4)+2\\ 4=4\text{ true}\\ y=\frac{1}{2}x+6\\ 4=\frac{1}{2}(-4)+6\\ 4=4\text{ true}\end{array}$

Hence, the solution of system is $(-4,4)$ .