Given:
[tex]\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-\frac{1}{4}x+2\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]
To solve for x and y:
Substitute the equation (2) in (1) we get,
[tex]\begin{gathered} x+4(-\frac{1}{4}x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}[/tex]
Therefore, the given system has infinitely many solutions.
