Problem Solving

Hello,

Can you please assist with this:

People who live in a certain apartment building subscribe only to magazines Q, R,
or S. Forty-five people live in the building and 39 people subscribe to at least one
magazine. Sixteen people subscribe to magazine Q, 19 people subscribe to
magazine R, and 22 people subscribe to magazine S. Eight people subscribe to
magazines Q and R, 7 people subscribe to magazines R and S, and 9 people subscribe
to magazines S and Q. The number of people who subscribe to the three magazines
equals the number of people who subscribe to none. How many people in the building
subscribe to only one magazine?

OA: 27


I tried to solve as follows:

a + b + c + d + e + f + g = 39

a + d + e + g = 16
b + d + f + g = 19
c + e + f + g = 22

a + b + d + e + f + g = 8
b + c + d + e + f + g = 7
a + c + d + e + f + g = 9

g = 45 - 39 = 6

a + b + c = ?


From above we have,

a + b + c + 2d + 2e + 2f + 3g = 57 - Eq. 1

2a + 2b + 2c + 3d + 3e + 3f + 3g = 24 - Eq. 2

a + b + c + d + e + f + g = 39 - Eq. 3


I was just wondering if this approach is correct since I get a negative answer when I solve the above 3 equations. Can you please assist?

Thanks,
Sri