Chapter 6.1, Problem 1P

To determine

To graph: the equations $y=2x+4,y=x+2$

Explanation of Solution

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

Graph:

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

For $y=2x+4$ :

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

Plot the points $(0,4),(1,6),(-1,2),(-2,0)$

For $y=x+2$ :

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

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

  

From the graph, it can be concluded that the two lines is intersecting at $A\left(-2,0\right)$

So, the solution of the system of equations $y=2x+4,y=x+2$ is $\left(-2,0\right)$

Now check whether $\left(-2,0\right)$ is a solution of the system of equations $y=2x+4,y=x+2$ .

Put $\left(-2,0\right)$ in $y=2x+4$

  $\begin{array}{l}0=2\left(-2\right)+4\\ \Rightarrow 0=-4+4\\ \Rightarrow 0=0\text{which}\text{is}\text{true}\end{array}$

So, $\left(-2,0\right)$ is a solution of the equation $y=2x+4$ .

Put $\left(-2,0\right)$ in $y=x+2$

  $\begin{array}{l}0=-2+2\\ \Rightarrow 0=0\text{which}\text{is}\text{true}\end{array}$

So, $\left(-2,0\right)$ is a solution of the equation $y=x+2$ .

Therefore,

  $\left(-2,0\right)$ is a solution of the system of equations is $y=2x+4,y=x+2$ .