Question

How many solutions does the system {y=x, y=tanx have?

Answer 1

make a sketch of their graphs and see where they intersect.
Here is one of the best websites for graphing ...
http://rechneronline.de/function-graphs/

enter:
x for the first graph
tan(x) for the second graph

change "Range x-axis from" -20 to 20
change "Range y-axis from" -50 to 50

As you can see there will be an infinite number of solutions
the obvious one is x=0
the next one is
another is appr 10.904
check:
y = x = 10.904
y = tan(10.904) = 10.9