Question

In the following exercises, solve the following system of equations by graphing

$$\begin{gathered} -x+2y=4 \\ y=\frac{1}{2}x-3 \end{gathered}$$

Short answer

There is no solution to this system.

Step-by-step solution

Step 1. Given information

The given equations are

$$\begin{gathered} -x+2y=4 \\ y=\frac{1}{2}x-3 \end{gathered}$$

Step 2. Finding the intersecting points 

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

$$\begin{gathered} -x+2y=4 \\ 2y=x+4 \\ y=1/2\times x+2 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}\mathrm{m}=1/2 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}\mathrm{b}=2 \\ \mathrm{Again}\mathrm{Solve}\mathrm{the}\mathrm{second}\mathrm{equation}\mathrm{for}\mathrm{y},\mathrm{and}\mathrm{find}\mathrm{the}\mathrm{slope}\mathrm{and}\mathrm{y}-\mathrm{intercept}. \\ \mathrm{y}=1/2\times \mathrm{x}-3 \\ \mathrm{Here}\mathrm{the}\mathrm{slope}\mathrm{is}\mathrm{m}=1/2 \\ \mathrm{And}\mathrm{the}\mathrm{y}-\mathrm{intercept}\mathrm{is}\mathrm{b}=-3 \end{gathered}$$

Step 3. Graph obtained

The lines are parallel.

Since no point is on both lines, there is no ordered pair that makes both equations true.

Therefore, there is no solution to this system.