SOLUTION: Write a linear system as a model of the following situation, then solve. Your school's star basketball player was excited about his play during the last game. He remembered that h

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Question 237908: Write a linear system as a model of the following situation, then solve.
Your school's star basketball player was excited about his play during the last game. He remembered that he scored 3-point shots, but couldn't recall how many free throws (worth 1 point each) and field goals (worth 2 points each) he scored. The scorekeeper said he had scored 20 times for 34 points.
How many field goals did he make? How many free throws did he make?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

If you meant to say that he scored three 3-point shots, then it works out this way.

Three 3-point shots is 3 shots worth 9 points, so the field goals and free throws have to account for 17 of the 20 shots and 25 of the 34 points.

Let represent the number of field goals and the number of free throws. Then is the number of field goal points and is the number of free throw points.





Multiply the first equation by -1:



Add this new equation to the original 2nd equation:



So, 8 field goals, and 17 - 8 = 9 free throws.

Check: 3 three-pointers for 9 points, 8 field goals for 16 points, and 9 free throws for 9 points. 3 + 8 + 9 = 20 and 9 + 16 + 9 = 34. Checks.

John