6) \( \begin{aligned} x-\frac{1}{2} y & =2 \\ y-2 x & =4\end{aligned} \)

To solve the system of equations, we can use substitution or elimination. Let’s solve for \( y \) in the first equation: From \( x - \frac{1}{2} y = 2 \), we can express \( y \) in terms of \( x \): \[ y = 2(x - 2) \Rightarrow y = 2x - 4 \] Now, substitute this expression for \( y \) into the second equation: \[ (2x - 4) - 2x = 4 \] Simplifying this gives: \[ -4 = 4 \] Since this results in a false statement, we infer that the system has no solution. Thus, the equations represent two parallel lines that never intersect. So, the final answer is that there are no solutions to the system of equations!