Two-Block Dynamics Problem: Determining Acceleration and Tension

[whitejac]

Homework Statement

Assuming no friction is on the plane or the pulleys and the pulley and rope have negligible mass... Determine the acceleration of each block and the tension in each cord. Block A weighs 100kg, Block B weighs 300kg.

Homework Equations

ΣF = ma
m_a = 100kg
m_b = 300kg

The Attempt at a Solution

ΣFx = ma_x = T₁ = 100a_x
ΣFy = ma_y = W - T₂ = 2943kg - T_{2 =} 300a_y
T₁=2T₂

I know that I have the relationships right, but I don't know exactly how to extract them...

 

[mechpeac]

What is the relationship between ax and ay? It is constrained motion, so you relate the two accelerations.

 

[whitejac]

I think I solved it this way based off of what my professor drew on the board but I need some clarity because I'm not quite sure how this can be...
if we assume:

a_x = 2a_y
^My professor's hint

then we have 4 relations and 4 unknowns. So:

T₁ = 2T₂
100a_x = 2[2943 - 300a_y]
50a_x = 2943 - 300a_y
a_x = 2a_y
50*2a_y = 2943 - 300a_y
400a_y = 2943

a_y = 7.3m/s^2
a_x = 14.8 m/s^2

**Edit**
This is an incorrect answer. The correct answer is 8.4m/s^2 for a_x which means somewhere my answer is almost 2 times larger.