Question

The Lakers scored a total of 80 points in a basketball game against the Bulls. The Lakers made a total of 37 two-point and three-point baskets. How many two-point shots did the Lakers make? Write a linear system of equations that can be used to solve this

Answer 1

The Lakers made 31 two-pointers and 6 three-pointers.

Explanation:

Let `x` be the number of two-point shots made and let `y` be the number of three-point shots made.

The Lakers scored a total of 80 points:
`2x+3y=80`

The Lakers made a total of 37 baskets:
`x+y=37`

These two equations can be solved:
(1) `2x+3y=80`
(2) `x+y=37`

Equation (2) gives:
(3) `x = 37-y`

Substituting (3) into (1) gives:
`2(37-y)+3y=80`
`74-2y+3y=80`
`y = 6`

Now let's just use the simpler equation (2) to get `x`:
`x+y=37`
`x+6=37`
`x = 31`

Hence, the Lakers made 31 two-pointers and 6 three-pointers.