Determine, in terms of \(k\), the coordinates of the point where the lines with the following equations intersect.
$$\begin{array} { r }
x + y = k
2 x - y = 1
\end{array}$$
Determine, in terms of \(k\), the coordinates of the points where the line \(\mathrm { x } + \mathrm { y } = \mathrm { k }\) crosses the curve \(y = x ^ { 2 } + k\).