Question

Graph each system and determine the number of solutions that it has. If it has one solution, name it.

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

Short answer

The graph of the system is

The number of solutions is 0.

Step-by-step solution

Step 1. Graph the system of equations.

The given system of equation is:

$x+2y=6$ … (1)

$3x+6y=8$ … (2)

The graph of two equations is drawn as below.

Step 2. Determine the number of solutions.

The slope of the given system of equation is:

$$\begin{gathered} x+2y=6 \\ y=-\frac{1}{2}x+3\dots \left(1\right) \end{gathered}$$

$$\begin{gathered} 3x+6y=8 \\ y=-\frac{3}{6}x+\frac{8}{6} \\ y=-\frac{1}{2}x+\frac{4}{3}\dots \left(2\right) \end{gathered}$$

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.

Step 3. Name the solutions, if possible.

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). Therefore, no solution of given system is there to label.