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