Chapter 6, Problem 8CR

To determine

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

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y=-2x-21\\ y=x-7\end{array}$

Calculation:

Find the intercepts

Consider the equation $y=-2x-21$

  $\begin{array}{l}y=0\Rightarrow x=-10.5\\ x=0\Rightarrow y=-21\end{array}$

Consider the equation $y=x-7$

  $\begin{array}{l}y=0\Rightarrow x=7\\ x=0\Rightarrow y=-7\end{array}$

Draw the line passing through the points $(-10.5,0)\&(0,-21)$

Draw the line passing through the points $(7,0)\&(0,-7)$

Graph:

The graph of given system is shown below.

  

Thus,

the point of intersection is the solution of the system. $(x,y)=(-11.667,-4.667).$

Verify the solution

  $\begin{array}{l}y=-2x-21\\ -11.667=-2(-4.667)-21\\ -11.667=-11.667\text{ true}\\ y=x-7\\ -11.667=-4.667-7\\ -11.667=-11.667\text{ true}\end{array}$

Hence, the solution of the system is $(x,y)=(-11.667,-4.667).$