KöMaL 2007 C917

Solve the following simultaneous equations: $x$+2$y$+3$z$+4$v$=$a$, $y$+2$z$+3$v$+4$x$=$b$, $z$+2$v$+3$x$+4$y$=$c$, $v$+2$x$+3$y$+4$z$=$d$, where $a$, $b$, $c$, $d$ are given real numbers.