Abasketball player scored 31 times during one game. he scored a total of 52 points, two for each two-point shot and one for each free throw. how many two-point shots did he make? how many free throws?

Let x = amount of two point shots, let y = free throw shots. We are going to use these to set up a system of equations. All of the shots combined equate to 31 so that's the first equation. The player's two-point shots and one-point free throws equate to 52 points so that's the second equation. 

x + y = 31
2x + y = 52

To cancel out the y-variables, I'm going to multiply the first equation by - 1

- x - y = - 31
2x + y = 52

Now combine like terms

x = 21

Now use this info to find the free throws by plugging it back in to either equation. I'll use the first one because it's easy.

21 + y = 31

Subtract 21 from both sides
y = 10

The player scored 21 two-point shots and 10 free throws. Sounds like some Russell Westbrook stats.