### Mapping a list to some variables for a system of equations

I have a list of integers $(a, b, c, d)$ and a system of equations, where each equation has two unknowns. My system looks like $(x0+x4, x1+x4, x2+x4, x3+x4).$ I am trying to evaluate the system in $(a,b,c,d)$. If I write $system(x0=1, x1=2, x3=1, x4=1)$, the system correctly outputs the result of each equation. Now, I would like to do something like $system(x0=a, x1=b, x3=c, x4=d)$ but without having to manually put the variables in. I have tried writing $system(list)$ but the number of variables and unknown doesn't match. Is there any way I can achieve this ?