College Algebra (6th Edition)

The first inequality represents the region INSIDE OR ON THE CIRCLE with radius $\sqrt{24}$, centered at $(-4,3)$ The second inequality represents the region OUTSIDE OR ON THE CIRCLE with radius $\sqrt{24}$, centered at $(-4,3)$ The intersection of the two solution sets is the circle itself, and it has an infinite number of points. So, there will be infinitely many solutions to the system.