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 system - of - equations result

Lian solved a system of linear equations representing the cost of gym memberships. The general form of the cost equation for a gym membership is $C = mx + b$, where $m$ is the monthly rate and $b$ is the one - time membership fee. When she got the equation $75 = 75$, it means the two equations in the system are equivalent in terms of the relationship between the variables. This implies that the monthly rates ($m$ values) are the same for both gyms. We don't have information about the one - time membership fees, so we can't say they are the same.

Answer:

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