\(P\) is the point of intersection of the lines \(y+x=1\) and \(3y+2x=1\). Find the co-ordinates of the point midway between \(P\) and the line \(y=2x+8\).

\(P\) is the point of intersection of the lines \(y+x=1\) and \(3y+2x=1\). Find the co-ordinates of the point midway between \(P\) and the line \(y=2x+8\).