Adult tickets for the school musical sold for $3.50 and student tickets sold for $2.50. three hundred twenty-one tickets for sold all together $937.50. how many of each kind of tickets were sold?

You cannot combine them in only one equation because they represent different things; so you will need two equations.
Now before we construct the two equations; lets set up our variables
Let a represent adult tickets
Let s represent student tickets
Now lets look at what we now about these two when thinking about them in money terms:
$3.50 per adult
$2.50 per student
Total made $937.50
Lets show it algebraically: 3.50a + 2.50s=$937.50
When thinking about the tickets in numbers we now the number sold were 321 so algebraically a + s = 321
Two equations; two variables; we can solve
a + s = 321
which is the same as
s= 321 - a
3.50a + 2.50s = 937.50
Since s = 321-a, we can substitute this into second equation:
3.50a + 2.50(321-a)=937.50
3.50a+802.5-2.50a=937.50
3.50a-2.50a+802.5=937.50
1.00a+802.5=937.50
a=135
Then s=321-135
s=186