8. \( \left\{\begin{array}{l}y-2 x=1 \\ 14 x-7 y=0\end{array}\right. \)

To solve the system of equations, we start with the first equation: \( y - 2x = 1 \). We can express \( y \) in terms of \( x \): \( y = 2x + 1 \). Next, we substitute this expression for \( y \) into the second equation \( 14x - 7y = 0 \): \[ 14x - 7(2x + 1) = 0 \] This simplifies to: \[ 14x - 14x - 7 = 0 \] which can be rearranged to: \[ -7 = 0 \] Since this is a contradiction, it indicates that the system of equations has no solution. The lines represented by the equations are parallel and will never intersect.