Answer
$\{(x,y)|x=4-2y,y\text{ is any real number}\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+2y=4\\
2x+4y=8
\end{cases}$
Use the elimination method. Multiply the first equation by $-2$ and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
-2(x+2y)=-2(4)\\
2x+4y=8
\end{cases}$
$\begin{cases}
-2x-4y=-8\\
2x+4y=8
\end{cases}$
$-2x-4y+2x+4y=-8+8$
$0=0$
As we got an identity, the system has infinitely many solutions.
We solve the first equation in terms of $y$:
$x=4-2y$
The solution set of the system is:
$\{(x,y)|x=4-2y,y\text{ is any real number}\}$
