In what way are graphs of systems of linear equations useful?

The graphs of equations within a system can tell you how many solutions exist for that system. Look at the images below. Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations.

It is very useful because we use Linear equations in our everyday life. Many people use linear equations every day, even if they do the calculations in their head without drawing a line graph.

The real importance of emphasizing graphing linear equations with your students, is that they should already know that any two points determine a line, so finding many pairs of values that satisfy a linear equation is easy: Find two pairs of values and draw a line through the points they describe.