Answer:
[tex]x+y=18 \\2x+3y=42[/tex]
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 = [tex]x[/tex]
Let number of 3-point shots taken = [tex]y[/tex]
Total number of shots taken = 18
Therefore, first equation can be written as:
[tex]x+y=18[/tex]
Total points scored = 42
Therefore, second equation can be written as:
[tex]2x+3y=42[/tex]
System of equations is:
[tex]x+y=18 .... (1)\\2x+3y=42 .... (2)[/tex]
Using elimination method to solve the system of equations.
Multiplying equation by 2 then subtracting it from equation (2):
[tex]3y - 2y = 42 - 36\\\Rightarrow y = 6[/tex]
By equation (1):
[tex]x+6=18\\\Rightarrow x = 12[/tex]
Therefore, Number of 2-point shots taken = 12
Number of 3-point shots taken = 6
