How many solutions does the nonlinear system of equations graphed below have?

How many solutions does the nonlinear system of equations graphed below have? 

Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system. 

Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.