Finding a variable in system of two equations

Question

I'm trying to solve a problem where i have those three equations:

$TR= \frac{Ia}{R}$,

$mg-T = ma$,

I know that $I=\frac{7}{2}MR^2 $

I need to find the variable $a$. The solution of the problem says that:

$$a= \frac{2mg}{7M+2m}$$

I know that to find $a$ i need to solve a system, but i don't understand how it got to that solution. Can someone guide me through the step to get to that solution?

Answer 1

$T = (mg-ma) = m(g-a)$

and $I = \frac{7MR^2}{2}$

So, $TR = \frac{Ia}{R} \implies TR^2 = Ia \implies m(g-a){R^2} = \frac{7}{2}MR^2a$

$\implies 2mg-2ma = {7M}a\implies a (2m+{7M}) = 2mg $

$$a = \frac{2mg}{7M+2m}$$

Answer 2

But $$a=\frac{TR^2}{I}$$ and $$a=\frac{mg-T}{m}$$ so it must be $$\frac{TR^2}{I}=\frac{mg-T}{m}$$