I am not sure what the expression is on the RHS, but I assume that you are given the correlation coefficient of the two random variables to be a fixed constantThe correlation between the two variables is: b = 10 – 2/3*a
Note that, as you displayed in a talbe, the number of support points of the joint probability mass function (6 unknowns)
Also, from the table you have degrees of freedom, i.e. you need to have 2 conditions to solve the joint. The four known conditions come from the fact that the sum of row/columns are equal to the marginal, and one of the five equations are redundant.
From the definition of correlation,
so you have the 5th equation. But you lack the 6th one to uniquely solve the table.