Chapter 6, Problem 15SGR

To determine

To graph:

The following equations of system and the set of solution:

  $\begin{array}{l}x+2y=6\\ 3x+2y=8\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}x+2y=6\\ 3x+2y=8\end{array}$

Graph:

  

Interpretation:

The given system of equation is:

  $x+2y=6$

  $y=-\frac{1}{2}x+3$........(1)

  $\begin{array}{l}3x+6y=8\\ y=-\frac{3}{6}x+\frac{8}{6}\end{array}$

  $y=-\frac{1}{2}x+\frac{4}{3}$........(2)

The graph of two equations is drawn as above. Now there is no intersection point of two straight lines shown by eq. (1) and (2).

Two lines are parallel to each other as the slope values from eq. (1) and (2) is same $m=-\frac{1}{2}$

Therefore, no solution of given system of equation.