Number of two-point shots: T
Number of free throws: F
The player scored 34 times during the game:
(1) T+F=34
She scored a total of 53 points:
(2) 2T+F=53
We have a system of 2 equations and 2 unkowns. If we substract equation (1) from equation (2)
(2T+F)-(T+F)=53-34
2T+F-T-F=19
T=19
Replacing T by 19 in equation (1):
(1) T+F=34
19+F=34
Solving for F:
19+F-19=34-19
F=15
Answers:
How many two-point shots did she make?
Answer: 19
How many free throws?
Answer: 15