Question

The basketball team scored 82 points from 2- points anf 3-points baskets. They make 38 baskets altogether. Let a represent the number of 2-points baskets and let b represent the number of 3-points baskets. Find the system of linear equations

Answer 1

Linear equations are
`a+b=38` and
`2a+3b=82`

Explanation:

Given : The basketball team scored 82 points from 2- points anf 3-points baskets. They make 38 baskets altogether.

To find : The system of linear equations

Solution :

Let a represent the number of 2-points baskets.

Let b represent the number of 3-points baskets.

They make 38 baskets altogether.

Equation form is
`a+b=38` .....[1]

The basketball team scored 82 points from 2- points basket ,3-points baskets.

Equation form is
`2a+3b=82` ......[2]

Linear equations are
`a+b=38` and
`2a+3b=82`

We solve the two equations,

Put a=38-b from [1] in [2]

`2(38-b)+3b=82`

`76-2b+3b=82`

`b=6`

Put back in [1]

`a+b=38`

`a+6=38`

`a=32`

Hence, There is 32 - 2 point basket and 6 - 3 points basket.

Answer 2

The System of linear equations are:

`2a+3b = 82`

`a+b=38`

Explanation:

Here, a represents the number of 2-points and b represent the number of 3-point basket.

As per the statement:

The basketball team scored 82 points from 2- points and 3-points baskets.

⇒
`2a+3b = 82`

It is also given that: They make 38 baskets altogether.

⇒
`a+b=38`

therefore, the system of linear equations are:

`2a+3b = 82`

`a+b=38`