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

Answer:

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

Number of 2-point shots taken = 12

Number of 3-point shots taken = 6

Step-by-step 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