imc

The second equation is $(|x|+|y|-4{)}^2=1$. We know that the graph of $|x|+|y|$ is a very simple diamond shape, so let's see if we can reduce this equation to that form: $$(|x|+|y|-4{)}^2=1⟹|x|+|y|-4=\pm 1⟹|x|+|y|=\{3,5\}.$$ We now have two separate graphs for this equation and one graph for the first equation, so let's put it on the coordinate plane: We see from the graph that there are $5$ intersections, so the answer is $\boxed{5}$.