Question

A famous basketball player scored 97 points in a high scool game, breaking a national record. She made 43 more 2-point baskets than 3-point baskets, and only 1 free throw. How many 2-point and 3-point baskets did she make?

Answer 1

x - 3pt baskets (he reaches 3x points)
y - 2pt baskets (he reaches 2y points)

We know, that y=x+43

97 - 1 free throw = 97 - 1 = 96
Sum of points: 96

3x + 2y = 96. Substitute to "y" an expression "x+43" :

3x + 2(x+43)=96
3x+2x+86=96
5x=10 |:5
x=2

So y=x+43=2+43=45

He has made 2 three points baskets and 45 two points baskets