Billy bought 2 sweatshirts and 3 t-shirts. His friend Jordan bout 3 sweatshirts and 3 t-shirts. Billy's bill was $35 and Jordan's bill was $45. What is the price of one t-shirt and what is the price of one sweatshirt?

Alright, denote sweatshirts by x and tshirts by y:
for billy: 2x+3y=35$
for jordan:3x+3y=45$
We need to get rid of one of the unknowns inorder to solve, therefore we will subtract the two equations from each other. This will get rid of the y variable(3y-3y=0)
2x+3y=35$
-
3x+3y=45$
=
-1x=-10$
we get rid of the negative, which leaves us with x=10$. Knowing this info, we can now easily calculate y:
2x+3y=35$
2(10)+3y=35$
20+3y=35$
3y=15
y=15/3
y=5
Hope this helps!