Finding the aceleration of a system

[undividable]

Homework Statement

I uploaded a picture with the problem from the textbook and its solution

Homework Equations

The relevante equations are in the attsmpt at a solution

The Attempt at a Solution

First of all, i understood the solution from the solution manual, but in my solution the only thing that is different is that i choose the positive x direction to be upwards the ramp , which is the oposite direction choosen in the solution manual
With said, i got the following equation for the NET force on each box
T-m1•g=m1•a
T-m2•g•sin55=m2•a
Doing the álgebra, i get a=-7.4, which is in the same direction as the a from the solution, but with a different magnitude, so my question is, are my 2 equations above wrong?

 

[Orodruin]

If you choise both masses' positive direction to be up then one accelerates in the negative direction when the other accelerates in the positive direction, i.e., $a_1 = -a_2$. You can therefore not use $a_1 = a_2 = a$ and must choose which of the accelerations you solve for.

 

[undividable]

If you choise both masses' positive direction to be up then one accelerates in the negative direction when the other accelerates in the positive direction, i.e., $a_1 = -a_2$. You can therefore not use $a_1 = a_2 = a$ and must choose which of the accelerations you solve for.

But shouldn't every choice of coordinate system give us a correct awnser?

 

[Orodruin]

It does, but you have to think about the directions. If you do the directions properly, you will get the right answer.