System of equation in two variables with extra pack

$x + (1 + k)y = 0$

$(1 - k)x + ky = 1 + k$

$(1 - k)x + ky = 1 + k$

In the above system of equations, $x = \frac{a}{b}$ and $y = \frac{-c}{d}$ , where a, b, c and d are positive integers. Find the value of the sum $a + b + c +d +k$ .

Details and assumption:

$\frac{a}{b}$ and $\frac{-c}{d}$ are in lowest term.