A basketball player scored 14 times during one game. She scored a total of 15 ​points, two for each​ two-point shot and one for each free throw. How many​ two-point shots did she ​make? How many free​ throws? She made two-point shots

The player made one two-point shot and 13 free throws.

Step-by-step explanation:

We can write a system of equations to model the situation.

Let t represent the number of two-point shots and let f represent the number of free throws made.

Since she scored a total of 14 times, the sum of two-pointers and free throws must equal 14. Hence:

And since she scored a total of 15 points and each two-pointers is worth two points and every free throw is worth one:

Solve the system. We can use elimination. From the first equation, multiply both sides by negative one:

We can add this to the second equation:

Simplify:

So, the player made only one two-point shot.

Using the first equation again, substitute one for t and solve for f:

Therefore, the player made one two-point shot and 13 free throws.