- Given the simultaneous equations
$$\begin{aligned}
& 2 x + y = 1
& x ^ { 2 } - 4 k y + 5 k = 0
\end{aligned}$$
where \(k\) is a non zero constant,
- show that
$$x ^ { 2 } + 8 k x + k = 0$$
Given that \(x ^ { 2 } + 8 k x + k = 0\) has equal roots,
- find the value of \(k\).
- For this value of \(k\), find the solution of the simultaneous equations.