Question

the basket ball team scored total of 97points. They made total of 42 two points and three points. how many two points and three points did they make??

Answer 1

let x be the number of 2 pointers made
let y be the number of 3 pointers made

the problem states that a total of 42 baskets were made. (thats how im interpreting the problem)
so,
x+y =42

The problem also states that the total score was 97 points,
now,
each two pointers "x" is worth 2 points so in terms of score, the two pointers will have a total score of "2x"
eac three pointers "y" is worth 3 points so in terms of score, the three pointers will have a total score of "3y"

and therefore, when you add up the total score of both two pointers and three pointers, it should be equal to 97. Hence,

2x+3y=97

So, now you have 2 equations, which I will solve by substitution
x+y=42
2x+3y=97

taking the first eq and solving for x
x=42-y
substituting that into the 2nd equation
2x+3y=97
2*(42-y) +3y=97

distributing
82-2y+3y=97

solving for y
y+82=97
y+82-82=92-82
y=10

now that we know y, we can solve for x using the first equation
x+y=42
substituting y to solve for x
x+10=42
x+10-10=42-10
x=32