Example5.1.14Parallel Lines

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

Figure5.1.15Graphs of \(y=2x-4\) and \(y=2x+1\)

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.)