Chapter 8.10, Problem 32STP

To determine

The solution of the system graph equations

  

Answer to Problem 32STP

The solution of the graph is $C=\left(-1,1\right)$

Explanation of Solution

Given:

There are four points are given as:

  $\begin{array}{l}A=\left(1,1\right)\\ B=\left(1,-1\right)\\ C=\left(-1,1\right)\\ D=\left(-1,-1\right)\end{array}$

And equations are as:

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

Calculation:

There are four points are given as:

  $\begin{array}{l}A=\left(1,1\right)\\ B=\left(1,-1\right)\\ C=\left(-1,1\right)\\ D=\left(-1,-1\right)\end{array}$

Put the given points in the graph equations:

For point $A=\left(1,1\right)$ :

  $\begin{array}{l}y=x,1=1\\ y=x+2,1=1+2=3\end{array}$

Eq. not satisfied.

For point $B=\left(1,-1\right)$ :

  $\begin{array}{l}y=-x,1=-1\\ y=x+2,1=-1+2=1\end{array}$

Eq. not satisfied.

For point $C=\left(-1,1\right)$ :

  $\begin{array}{l}y=-x,-1=-1\\ y=x+2,-1=-1+2=-1\end{array}$

Eq. not satisfied.

For point $D=\left(-1,-1\right)$ :

  $\begin{array}{l}y=-x,-1=-1\\ y=x+2,-1=-1+2=1\end{array}$

Eq. not satisfied.

So, the points of $C=\left(-1,1\right)$ satisfied the graphed eq. $y=-x,y=x+2$ .

Conclusion:

Hence, point solution which satisfied the graphed eqn. is $C=\left(-1,1\right)$ .