Chapter 6, Problem 4CR

To determine

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

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y=3x+13\\ y=x-3\end{array}$

Calculation:

Find the intercepts

Consider the equation $y=3x+13$

  $\begin{array}{l}y=0\Rightarrow x=-4.3\\ x=0\Rightarrow y=13\end{array}$

Consider the equation $y=x-3$

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

Draw the line passing through the points $(-4.3,0)\&(0,13)$

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

Graph:

The graph of given system is shown below.

  

Thus,

the point of intersection is the solution of the system. $(x,y)=(-8,-11)$

Verify the solution

  $\begin{array}{l}y=3x+13\\ -11=3(-8)+13\\ -11=-11\text{ true}\\ y=x-3\\ -11=-8-3\\ -11=-11\text{ true}\end{array}$

Hence, the solution of the system is $(x,y)=(-8,-11)$