SOLUTION: System of Linear Equation question : there are 8173 students in a college such that the number of girls is 421 more than the number of boys. How many of each are there ?

g + b = 8173,   (1)
g - b =  421.   (2)

Every time when you see two equations like these, add them. In your case you get

2g = 8173 + 421,   or

2g = 8594.

Hence, g =  = 4297.

There are 4297 girls in the college.

Now, from (1), b = 8173 - g = 8173 - 4297 = 3876.

Answer. 4297 girls and 3876 boys.