Answer
$\{(x,y)|y=3x-7,x\text{ is any real number}\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
3x-y=7\\
9x-3y=21
\end{cases}$
Use the elimination method. Multiply the first equation by $-3$ and add it to the second equation to eliminate $y$ and determine $x$:
$\begin{cases}
-3(3x-y)=-3(7)\\
9x-3y=21
\end{cases}$
$\begin{cases}
-9x+3y=-21\\
9x-3y=21
\end{cases}$
$-9x+3y+9x-3y=-21+21$
$0=0$
As we got an identity, the system has infinitely many solutions.
We solve the first equation in terms of $x$:
$3x-y=7$
$y=3x-7$
The solution set of the system is:
$\{(x,y)|y=3x-7,x\text{ is any real number}\}$
