Question

Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5

2 months

5 months

3 months

4 months

Answer 1

It would take 2 months for the membership of both clubs to be the same

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost of dues over x months, hence given that:

y = 3x - 5     (1)

Also:

4x - 3y = 5

y = (4x - 5)/3      (2)

For the membership of both clubs to be the same:

3x - 5 = (4x - 5)/3    

9x - 15 = 4x - 5

x = 2

It would take 2 months for the membership of both clubs to be the same

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