Chapter 6, Problem 2CT

To determine

To graph: equations $x+3y=12,x=y-8$

Explanation of Solution

Given information: equations are $x+3y=12,x=y-8$

Graph:

First find points that can be used to plot the graph of the equations $x+3y=12,x=y-8$

For $x+3y=12$ :

  $\begin{array}{l}x+3y=12\\ \Rightarrow x=12-3y\end{array}$

  $\begin{array}{l}y=2;x=12-6=6\\ y=3;x=12-9=3\\ y=4;x=12-12=0\\ y=0;x=12-0=12\\ y=5;x=12-15=-3\end{array}$

Plot the points 3 $\left(6,2\right),\left(3,3\right),\left(0,4\right),\left(12,0\right),\left(-3,5\right)$

For

  $x=y-8$

  $\begin{array}{l}y=0;x=0-8=-8\\ y=3;x=3-8=-5\\ y=4;x=4-8=-4\\ y=6;x=6-8=-2\\ y=5;x=5-8=-3\end{array}$

Plot the points $\left(-8,0\right),\left(-5,3\right),\left(-4,4\right),\left(-2,6\right),\left(-3,5\right)$

  

As the lines are intersecting, the solution of the given system of equations is unique. This is the system of equations has one solution.

Solution is $\left(-3,5\right)$