Chapter 5.4, Problem 18E

To determine

To calculate:

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

Answer to Problem 18E

Solution for given linear equation has no solution.

Explanation of Solution

Given information:

  $\begin{array}{l}y=-6x-2\\ 12x+2y=-6\end{array}$

Calculation:

Given equations are:

  $\begin{array}{l}y=-6x-\mathrm{2...}\left(i\right)\\ 12x+2y=-\mathrm{6..}\left(ii\right)\end{array}$

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

  $\begin{array}{l}12x+2y=-6\\ 2y=-6-12x\end{array}$

Divide by $2$ on both sides,

  $\begin{array}{l}\frac{2y}{2}=\frac{-6}{2}-\frac{12x}{2}\\ y=-3-6x\end{array}$

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

The slopes of lines are $-6$ respectively for both equations and $y-$ intercept is $-2,-3$

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 same slope but different $y-$ intercept thus it represents parallel lines.

Parallel lines do not intersect the system has no solution.

Thus lines are coincident shown as below: