To solve the system of equations:
- \(3x + y = 30\)
- \(x - 3y = 0\)
We can use the substitution or elimination method. Here, I will use substitution.
From the second equation, we can express \(x\) in terms of \(y\):
\[ x = 3y \]
Now we can substitute \(x\) in the first equation:
\[ 3(3y) + y = 30 \]
This simplifies to:
\[ 9y + y = 30 \]
Combine like terms:
\[ 10y = 30 \]
Now, divide both sides by 10:
\[ y = 3 \]
Now that we have \(y\), we can substitute it back into the equation \(x = 3y\) to find \(x\):
\[ x = 3(3) = 9 \]
Thus, the solution to the system of equations is:
\[ x = 9, \quad y = 3 \]
Or in ordered pair notation:
\[ (9, 3) \]