Chapter 6.1, Problem 26PPE

To determine

To graph: the system of equations $y=2x-2,2y=4x-4$

Explanation of Solution

Given information: The system of equations is $y=2x-2,2y=4x-4$

Graph:

First find the points that can be used to plot the graphs of equations $y=2x-2,2y=4x-4$

For $y=2x-2$ :

  $\begin{array}{l}x=0;y=0-2=-2\\ x=1;y=2-2=0\\ x=2;y=4-2=2\\ x=3;y=6-2=4\end{array}$

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

For $2y=4x-4$ :

At $x=0$ :

  $2y=0-4\Rightarrow 2y=-4\Rightarrow y=-2$

At $x=1$ :

  $2y=4-4\Rightarrow 2y=0\Rightarrow y=0$

At $x=2$ :

  $2y=8-4\Rightarrow 2y=4\Rightarrow y=2$

At $x=3$ :

  $2y=12-4\Rightarrow 2y=8\Rightarrow y=4$

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

  

The system of linear equations has infinite solutions if the graphs of the two lines represented by the equations are coincident.

From the graph drawn above, it can be observed that the graphs of the equations $y=2x-2,2y=4x-4$ are coincident.

So,

The system of equations $y=2x-2,2y=4x-4$ has infinite solutions.