lian is deciding which of two gyms to join. each gym charges a monthly rate plus a one - time membership…

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.

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.

Answer

Explanation:

Step1: Recall system - of - equations concept

When solving a system of linear equations and getting an identity like (a = a) (in this case (75=75)), it means the two equations are equivalent.

Step2: Relate to gym - cost equations

Let the cost of the first gym be (C_1 = m_1x + f_1) and the second gym be (C_2=m_2x + f_2), where (m) is the monthly rate, (x) is the number of months, and (f) is the membership fee. If (C_1 = C_2) results in an identity, then (m_1=m_2) and (f_1 = f_2).

Answer:

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