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?

a. One gym charges $75 per month.
b. Each gym charges $75 per month.
c. Both gyms charge the same monthly rate and the same membership fee.
d. Both gyms charge the same monthly rate, but not the same membership fee.

Answer 1

Both gyms charge the same monthly rate and the same membership fee.

Explanation:

Answer 2

The resulting equation 75 = 75 is an identity; this tells that the two equations of the system are equivalent, this is they both represent the same function. So, Lian can conclude that (option c) both gyms charge the same monthly rate and the same membership fee.