Question

lian is deciding which of two gyms to join. each gym charges a monthly rate plus a one - time membership fee. lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. in her work, she substituted an expression for one variable and solved for the other. this resulted in the equation 75 = 75. what can lian conclude? one gym charges $75 per month. each gym charges $75 per month. both gyms charge the same monthly rate and the same membership fee. both gyms charge the same monthly rate, but not the same membership fee.

Explanation:

Step1: Analyze the equation result

The equation 75 = 75 is an identity. In the context of comparing gym - membership costs (where the cost is modeled as a linear equation of the form $y=mx + b$, with $m$ being the monthly rate and $b$ being the one - time membership fee), when we get an identity after substitution in a system of linear equations, it means the two equations are equivalent in terms of the relationship between the variables. This implies that the monthly rates are the same. We don't have information about the membership fees from this equation alone.

Answer:

Each gym charges the same monthly rate, but not the same membership fee.