Chapter 5.4, Problem 20E

To determine

To calculate:

Given system of linear equation has one, infinite or no solution using graph.

Answer to Problem 20E

Solution for given linear equation has one solution.

Explanation of Solution

Given information:

  $\begin{array}{l}-7x+7y=1\\ 2x-2y=-18\end{array}$

Calculation:

Given equations are:

  $\begin{array}{l}-7x+7y=\mathrm{1...}\left(i\right)\\ 2x-2y=-\mathrm{18...}\left(ii\right)\end{array}$

After simplifying eq. $\left(ii\right)$ ,

  $\begin{array}{l}-7x+7y=1\\ 7y=1+7x\end{array}$

Divide by $7$ on both sides,

  $\begin{array}{l}\frac{7y}{7}=\frac{1}{7}+\frac{7x}{7}\\ y=0.15+x\end{array}$

Another equation is:

  $2x-2y=-\mathrm{18...}\left(ii\right)$

After simplifying eq. $\left(ii\right)$ ,

  $\begin{array}{l}2x-2y=-18\\ -2y=-18-2x\end{array}$

Divide by $-2$ on both sides,

  $\begin{array}{l}\frac{-2y}{-2}=\frac{-18}{-2}-\frac{2x}{-2}\\ y=-9-x\end{array}$

For finding out the number of solutions of the system of equation,

The slopes of lines are $1,-1$ respectively for both equations and $y-$ intercept is $0.15,-9$

Since the lines are in slope and $y-$ intercept form as $y=mx+c$ , where $m=$ slope of line and $\left(0,b\right)$ be the $y-$ intercept.

As both equations has different slop and different $y-$ intercept thus it represents intersecting lines.

Thus lines are coincident shown as below: