Answer
$\left\{\left(x,\dfrac{10-2x}{5}\right)|x\text{ is any real number}\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x+5y=10\\
4x+10y=20
\end{cases}$
Use the elimination method. Multiply the first equation by -2 and add it to the second to eliminate $y$ and find $x$:
$-2(2x+5y)+4x+10y=-2(10)+20$
$-4x-10y+4x+10y=-20+20$
$0=0$
We got an identity; therefore the system has infinitely many solutions.
Determine $y$ in terms of $x$:
$2x+5y=10$
$5y=10-2x$
$y=\dfrac{10-2x}{5}$
The solution set is:
$\left\{\left(x,\dfrac{10-2x}{5}\right)|x\text{ is any real number}\right\}$
