The ‘standard’ way is to substitute into one equation from the others, eliminating all but one variable, then substituting that known back into the others, thus solving the simultaneous system, and thus the sum once all unknowns are known. A more elegant approach when the number of variables gets hard to handle like a million or so is inversion of the matrix of coefficients operating on the RHS of the system yielding the unknowns in one fell swoop. And yes D=17, C=7, R=3, and thus Σ=27.
Viola.