Solving simultaneous equation for discrete math

Question

equation 1: 0 = x + y

equation 2: 1 = xr + ys

Where r = (1 + sqrt(5)) / 2, and s = (1 - sqrt(5)) / 2

my approach is to set equation 2 to 0 = xr + ys - 1 . Then, xr + ys -1 = x + y

Im not sure where to go from here.

Answer 1

$$\begin{cases} x+y=0 \\ xr+ys=1\end{cases}$$

$x+y=0\implies x=-y$. Substitute this in for $y$ in the second equation. $$xr-xs=1\implies x=\dfrac{1}{r-s}$$

Since $y=-x \implies y=\dfrac{-1}{r-s}$. Hence $\left(x,y\right)\mapsto\left(\dfrac{1}{r-s}, \dfrac{-1}{r-s}\right)$ is the solution.