Question

Gladys scored 42 points in a basketball game. She only took 2-point shots and 3-point shots. She made a total of 18 shots. Write a system of equations to find the number of 2-point shots and 3-point shots Gladys made. Let LaTeX: xx represent the number of 2-point shots and LaTeX: yy represent the number of 3-point shots that Gladys made.

Answer 1

`x+y=18 \\2x+3y=42`

Number of 2-point shots taken = 12

Number of 3-point shots taken = 6

Explanation:

Total number of points scored by Gladys = 42

Only 2-point and 3-point shots are taken by Gladys.

Let number of 2-point shots taken =
`x`

Let number of 3-point shots taken =
`y`

Total number of shots taken = 18

Therefore, first equation can be written as:

`x+y=18`

Total points scored = 42

Therefore, second equation can be written as:

`2x+3y=42`

System of equations is:

`x+y=18 .... (1)\\2x+3y=42 .... (2)`

Using elimination method to solve the system of equations.

Multiplying equation by 2 then subtracting it from equation (2):

`3y - 2y = 42 - 36\\\Rightarrow y = 6`

By equation (1):

`x+6=18\\\Rightarrow x = 12`

Therefore, Number of 2-point shots taken = 12

Number of 3-point shots taken = 6