Greggory is trying to raise money for his​ school's football team by selling​ T-shirts and sweatshirts. The football team will get​ $3 for each sweatshirt sold and​ $4 for each​ T-shirt sold. The rest of the money goes to paying for the items to be sold. Greggory manages to sell a total of 121 items and the team ends up getting​ $406.

# of sweatshirts sold = x = 78
# of t-shirts sold = y = 43

We know:
x + y = 121
3x + 4y = 406

Solve the first equation for x in terms of y, then substitute that into the second equation.

x = 121 - y

3(121 - y) + 4y = 406
363 - 3y + 4y = 406
y + 363 = 406
y = 43

Then solve for x

x = 121 - y
x = 121 - 43
x = 78

Check the math:
3(78) + 4(43) = 234 + 172 = 406