Question

There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club.
a. Write a system of linear equations that represents this situation. Let x represent the number of students in the drama club and y represent the number of students in the yearbook club.

Answer 1

Given:
64 total students
x = drama club students
y = yearbook club students

x = y + 10
y = 64 - x

y = 64 - x
y = 64 - (y + 10)
y = 64 - y - 10
y + y = 64 - 10
2y = 54
2y/2 = 54/2
y = 27

x = y + 10
x = 27 + 10
x = 37 

To check:

x + y = 64
37 + 27 = 64
64 = 64