###### Example5.1.14Parallel Lines

Let's look at the graphs of two lines with the same slope, \(y=2x-4\) and \(y=2x+1\text{:}\)

For this system of equations, what is the solution? Since the two lines have the same slope they are parallel lines and will never intersect. This means that there is *no solution* to this system of equations. We write the solution set as \(\emptyset\text{.}\) (This is a special symbol to represent a set with nothing in it, not the number zero.)