To solve the system of equations, we have:
- \( x - 3y = 18 \)
- \( 7x - 5y = 46 \)
First, we can solve the first equation for \( x \):
\[ x = 3y + 18 \]
Next, we can substitute this expression for \( x \) into the second equation:
\[ 7(3y + 18) - 5y = 46 \]
Now, distribute \( 7 \):
\[ 21y + 126 - 5y = 46 \]
Combine like terms:
\[ 16y + 126 = 46 \]
Subtract 126 from both sides:
\[ 16y = 46 - 126 \] \[ 16y = -80 \]
Now, divide by 16:
\[ y = -5 \]
Now that we have \( y \), we can substitute \( y = -5 \) back into our expression for \( x \):
\[ x = 3(-5) + 18 = -15 + 18 = 3 \]
So, the solution to the system of equations is:
\[ (x, y) = (3, -5) \]
The answer to the system of equations is
\[ \boxed{(3, -5)} \]