.
 a +  c = 101,   ("a" for the number of adults, and "c" for the number of child)
7a + 4c = 491,
if you want solve it using the system of two equations with to unknowns.
Or simply
7a + 4(101-a) = 491,
if you want to solve it as a single equation.
From the last equation 
7a + 404 - 4a = 491,
3a = 491 - 404,
3a = 87,  --->  a =  = 29.
Answer.  29 adults and 101 - 29 = 72 children.
 = 29.
Answer.  29 adults and 101 - 29 = 72 children.