A basketball player scored 8 times in a game for a total of 12 points. Two points are awarded for each two-point shot, and one point is awarded for each free throw. The problem asks us to determine the number of two-point shots and free throws the player made.

1. Problem Description

A basketball player scored 8 times in a game for a total of 12 points. Two points are awarded for each two-point shot, and one point is awarded for each free throw. The problem asks us to determine the number of two-point shots and free throws the player made.

2. Solution Steps

Let $x$ be the number of two-point shots made, and let $y$ be the number of free throws made.

We can set up a system of two equations based on the given information:

The total number of shots made is 8:

$x + y = 8$

The total number of points scored is 12:

$2x + y = 12$

We can solve this system of equations. We can solve for $y$ in the first equation:

$y = 8 - x$

Substitute this expression for $y$ into the second equation:

$2x + (8 - x) = 12$

$2x + 8 - x = 12$

$x + 8 = 12$

$x = 12 - 8$

$x = 4$

Now, substitute the value of $x$ back into the equation for $y$:

$y = 8 - x = 8 - 4 = 4$

So, the player made 4 two-point shots and 4 free throws.

3. Final Answer

He made 4 two-point shots.