X | Y
-2 | 9
-1 | 6
0 | 3
1 | 0
2 | -3
She made the mistake in step 4
She should have divided by -2 not just 2 alone
Let
x--------> the number of sessions
y-------> the total payment
we know that
without membership:
--------> equation 
with membership:
--------> equation 
using a graph tool------> resolve the system of equations
see the attached figure
the solution is the point 
that means
For 
the cost is
in both forms
so
to justify buying the membership

therefore
<u>the answer is</u>
