Chapter 6, Problem 3CT

To determine

To graph: equations $x+y=5,x+y=-2$

Explanation of Solution

Given information: equations are $x+y=5,x+y=-2$

Graph:

First find points that can be used to plot the graph of the equations $x+y=5,x+y=-2$

For $x+y=5$ :

  $y=5-x$

  $\begin{array}{l}x=0;y=5-0=5\\ x=1;y=5-1=4\\ x=2;y=5-2=3\\ x=3;y=5-3=2\end{array}$

Plot the points $\left(0,5\right),\left(1,4\right),\left(2,3\right),\left(3,2\right)$

For $x+y=-2$ :

  $y=-2-x$

  $\begin{array}{l}x=0;y=-2-0=-2\\ x=1;y=-2-1=-3\\ x=2;y=-2-2=-4\\ x=-1;y=-2+1=-1\end{array}$

Plot the points $\left(0,-2\right),\left(1,-3\right),\left(2,-4\right),\left(-1,-1\right)$

  

As the lines are parallel, the given system of equations has no solution.