The given system is
[tex]\mleft\{\begin{aligned}4x+2y=16 \\ 2x+y=4\end{aligned}\mright.[/tex]We multiply the second equation by -2, then we sum equations
[tex]\begin{gathered} \mleft\{\begin{aligned}4x+2y=16 \\ -4x-2y=-8\end{aligned}\mright. \\ 0x+0y=8 \\ 0=8 \end{gathered}[/tex]Since 0 is not equal to 8, we deduct that the system has no solutions.
