Chapter 8.7, Problem 52HP

To determine

To find: System of linear equations and solution.

Answer to Problem 52HP

Linear equations are

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

Solution is $\left(2,-1\right)$

Explanation of Solution

From the given table taking two $\left(x,y_1\right)$ points

We get

  $\left(-4,11\right)$ And $\left(4,-5\right)$

Lines formed by above points are

  $\begin{array}{l}y-11=\frac{-5-11}{4-\left(-4\right)}\left(x-\left(-4\right)\right)\\ \Rightarrow y-11=\frac{-16}{8}\left(x+4\right)\\ \Rightarrow y-11=-2\left(x+4\right)\\ \Rightarrow y-11=-2x-8\\ \Rightarrow 2x+y=3\end{array}$

From the given table taking two $\left(x,y_1\right)$ points

We get

  $\left(-4,-7\right)$ And $\left(4,1\right)$

Lines formed by above points are

  $\begin{array}{l}y-\left(-7\right)=\frac{1-\left(-7\right)}{4-\left(-4\right)}\left(x-\left(-4\right)\right)\\ \Rightarrow y+7=\frac{1+7}{4+4}\left(x+4\right)\\ \Rightarrow y+7=\frac{8}{8}\left(x+4\right)\\ \Rightarrow y+7=x+4\\ \Rightarrow x-y=3\end{array}$

Therefore,

Linear equations are

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

On graphing both linear equations

We get

  

Here blue line represents the graph of $x-y=3$ and red line represents the graph of $2x+y=3$ .

Therefore,

Point of intersection of both lines is the solution that is $\left(2,-1\right)$