Question

10. MAAL has had 10 members in their Spanish club since 2000. Over the next several years, the club

increased by an average of 1 member per year. In the same original year, MAAL had 4 members in their chorus.
The chorus saw an increase of 3 members per year.
1) Create a system of equations based on the question.
2) Graphically solve the system.
3) Explain in detail what each coordinate of the point of
intersection of these equations means in the context of this
problem.

Answer 1

To answer the question, two linear equations are constructed: y = x + 10 for the Spanish club and y = 3x + 4 for the chorus. The system is graphically solved by plotting these equations and finding their intersection, which reveals the year and the number of members when both clubs have equal members.

Step-by-step explanation:

To create a system of equations based on the question, we will define x as the number of years since 2000, and y as the number of members in each club.

For the Spanish club, the initial number of members in 2000 was 10, and it increased by 1 member per year. Hence, the equation for the Spanish club is y = x + 10.

For the chorus, the initial number of members was 4, and it increased by 3 members per year. Therefore, the equation for the chorus is y = 3x + 4.

To graphically solve the system, we draw two lines representing these equations on a coordinate plane. The point where they intersect is the solution to the system.

The coordinate of the intersection tells us the year since 2000 (x-coordinate) and the number of members (y-coordinate) when the Spanish club and the chorus will have the same number of members.