Question

A basketball team scored a total of 97 points in a basketball game. They made a total of 42 two-point and three-point baskets. How many two-point baskets did they make? How many three-point baskets did they make?

Answer 1

Answer:

y = 13

they made 29 two points

and 13 three points

Answer 2

Solution of the given system of equations are two point baskets = 29 and three point baskets = 13.

What is the system of equations?

" A system of equations is a finite set of equations for which we find the common solution."

According to the question,

x represents the two point baskets

y represents the three point baskets

Situation 1:  Total of 97 points scored by team in a basketball game, which can be represented by equation:

$2x + 3y =97$                    ____(1)

Situation2: Total of 42 two-point and three-point baskets made by team, which can be represented by equation:

$x + y =42$                      

$y = 42-x$                       _____(2)

Substitute the value of 'y' from system of equations (2) to (1)  we get,

$2x + 3(42-x) =97$

⇒$2x +126-3x =97$

⇒$x= 126-97$

⇒$x= 29$

Two point baskets = 29

Substitute the value of 'x' in (2) we get,

$y = 42-29$

⇒$y=13$

Three point baskets = 13

Hence, solution of the given system of equations are two point baskets = 29 and three point baskets = 13.

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