Two weights with masses of 2 and 4 kg, connected by an inextensible thread, are lifted vertically by a force of 84 N

Two weights with masses of 2 and 4 kg, connected by an inextensible thread, are lifted vertically by a force of 84 N applied to the first weight. Determine the acceleration with which the weights are moving and the tension in the thread.

F − m1g − T = m1a;
F − m1g − T = m1a; (1)
T − m2g = m2a. (2)
Adding these equations, we get:
F− (m1 + m2) g = (m1 + m2) a.
From here we find the acceleration of loads:
a = Fm1 + m2 − g.
T = m2 (g + a) = Fm2m1 + m2.
a = 84/6 -10 = 4 m / s ^ 2
T = 84 * 4/6 = 56 N.
Answer: 4 m / s ^ 2; 56 N.