Chapter 6, Problem 6CR

To determine

To solve: the given system using graphing and to check the solution.

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y=2x+3\\ y=\frac{1}{3}x-2\end{array}$

Calculation:

Find the intercepts

Consider the equation $y=2x+3$

  $\begin{array}{l}y=0\Rightarrow x=-1.5\\ x=0\Rightarrow y=3\end{array}$

Consider the equation $y=\frac{1}{3}x-2$

  $\begin{array}{l}y=0\Rightarrow x=6\\ x=0\Rightarrow y=-2\end{array}$

Draw the line passing through the points $(-1.5,0)\&(0,3)$

Draw the line passing through the points $(6,0)\&(0,-2)$

Graph:

The graph of given system is shown below.

  

Thus,

the point of intersection is the solution of the system. $(x,y)=(-3,3)$

Verify the solution

  $\begin{array}{l}y=2x+3\\ -3=2(-3)+3\\ -3=-3\\ y=\frac{1}{3}x-2\\ -3=\frac{1}{3}(-3)-2\\ -3=-3\end{array}$

Hence, the solution of the system is $(x,y)=(-3,3)$