I need to carry out multivariate linear regression such that the values of dependent variables are different for each of the independent variables. How do I go about doing it

Say we have two independent variables : Y(1), Y(2) such that Y(1) = B(1) + w1*V1(1) + w2*V2(1) + ... + w6*V6(1) and Y(2) = B(2) + w1*V1(1) + w2*V2(1) + ... + w6*V6(1) We are trying to find a function that will fit our (Y,V) data using multivariate regression. The goal is to find a vector [B w1 w2 … w6] that satisfies a least-squares fit to Y , now all the solutions online have the dependent variable( v ) having the same values for Y(1) and Y(2) but in my dataset the values for each independent variables are different .How do I solve such a question ?