Solve this system of equations please it’s giving me fits

Given the system of equations below
[tex]\begin{gathered} y=\frac{1}{2}x+\frac{7}{4}\ldots(1) \\ 2x-4y=1\ldots(2) \end{gathered}[/tex]Using the substitution method
Substitute the value of y in equation (1) for y in equation (2)
[tex]\begin{gathered} 2x-4y=1 \\ 2x-4(\frac{1}{2}x+\frac{7}{4})=1 \\ 2x-2x-7=1 \\ -7=1 \end{gathered}[/tex]The graph of the syste
Hence, there is no solution