Chapter 2.1, Problem 17E

To determine

To find: of the system of given equations by graphing.

Answer to Problem 17E

No solution

Explanation of Solution

Given information:

  $\begin{array}{l}x+3y=0\mathrm{...}\left(1\right)\\ 2x+6y=5\mathrm{...}\left(2\right)\end{array}$

Calculation:

Convert equation (1) into slope intercept form to evaluate the value of slope and y-intercept as follows:

  $\begin{array}{c}x+3y=0\\ 3y=-x+0\\ y=-\frac{1}{3}x+0\end{array}$

Thus, the value of slope is $-\frac{1}{3}$ and y-intercept is $0$ .

Convert equation (2) into slope intercept form to evaluate the value of slope and y-intercept as follows:

  $\begin{array}{c}2x+6y=5\\ 6y=-2x+5\\ y=-\frac{2}{6}x+\frac{5}{6}\\ y=-\frac{1}{3}x+\frac{5}{6}\end{array}$

Thus, the value of slope is $-\frac{1}{3}$ and y-intercept is $\frac{5}{6}$ .

Since, the slope of both the lines is same. So, the lines are parallel and they will not intersect each other. Thus, there is no solution for these equations.

The graph of equation (1) and (2) is as follows:

  

As the lines do not intersect each other. Thus, there is no solution for these equations.