Answer
No Solution.
Work Step by Step
To solve the system $\begin{cases}x-2y=4 \\ 2x-4y=4 \\ \end{cases},$ we perform elementary row operations on the corresponding augmented matrix to obtain an equivalent matrix with $1s$ along the main diagonal (if possible).
The corresponding augmented matrix is
$$\left[
\begin{array}{cc|c}
1 & -2 & 4 \\
2 & -4 & 4\\
\end{array}
\right].$$
We replace Row_2 with Row_2-2*Row_1 to obtain the equivalent matrix
$$\left[
\begin{array}{cc|c}
1 & -2 & 4 \\
0 & 0 & -4\\
\end{array}
\right].$$
Now, we see in Row_2 that every entry but the last entry is a zero. This means the system of equations corresponding to this matrix is inconsistent (i.e., has no solutions).
To see this, we form the system of equations corresponding to this matrix:
$$\begin{cases}x-2y=4 \\ 0=-4 \\ \end{cases}.$$
We see $0=-4$ is false for all values of $x$ and/or $y$. So this system of equations has no solutions.
