Combine the expressions for tension and solve for acceleration

[asusal]

1. Derive an equation for the acceleration of both the cart and suspended mass in
terms of both masses (Mc and Ms ), the angle of the incline (θ), and the acceleration due to gravity (g).

Homework Equations

Fx=
T - Mgsin θ = Ma

T = Mgsin θ + Ma
Fy
T = mg - ma

Combine the expressions for Tension and solve for the acceleration.

A= (mg - Mg sin θ / M + m )

https://imgur.com/a/Okk79t9 (I know in the picture it's already derived in the correct form I just want to know how they got that correctly.)[/B]

The Attempt at a Solution

So I combined the equations

T= (ms*g-mc*g*sin(θ) ) / ( mc + mg)

T= ms (g- (ms*g-mc*g*sin θ/ mc+ms) )

[/B]
I'm assuming I factor MS and common denom but it doesn't seem like I'm doing this correctly.
Any help would be appreciated!

Thanks.

 

[CWatters]

Uploaded the image for future readers..

 

[CWatters]

So I combined the equations
T= (ms*g-mc*g*sin(θ) ) / ( mc + mg)
T= ms (g- (ms*g-mc*g*sin θ/ mc+ms) )

I'm assuming I factor MS and common denom but it doesn't seem like I'm doing this correctly.
Any help would be appreciated!

Can you show more of your working?

Why introduce ms and mc ? In the image they use "M" for the mass of the cart and "m" for the suspended mass. I suggest you stick to that notation.

 

[CWatters]

Hint: When you combine two equations you can frequently eliminate one unknown variable. Which unknown doesn't appear in the final equation given to you?