Chapter 8.4, Problem 11E

To determine

To Find: Whether the graph of pair of equation is parallel, perpendicular or neither.

Answer to Problem 11E

Graph of Pair of equation is parallel.

Explanation of Solution

Given information:

The pair of equation:

  $\begin{array}{l}3x+y=7\\ y=-3x+2\end{array}$

Formula used: -

Slope form of line: $y=mx+c$ .

Where $m$ is the slope of line, and $c$ is the $y$ -intercept when $x=0$ .

For parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$ .

For perpendicular lines with slope $m_1$ and $m_2$ , $m_1{m}_2=-1$ .

  $\begin{array}{l}3x+y=7\\ y=-3x+2\end{array}$

Converting the pair of equation into Slope form of line: $y=mx+c$ .

  $\begin{array}{l}3x+y=7\\ y=-3x+7\end{array}$

So, $m_1=-3$

  $y=-3x+2$

  $m_2=-3$

For parallel lines with slope $m_1$ and $m_2$ , $m_1=m_2$ .

  $-3=-3$

  $m_1=m_2$

So, graph of Pair of equation is parallel.