To solve the system of equations:
- \( x - 3y = 18 \) (Equation 1)
- \( 7x - 5y = 46 \) (Equation 2)
We can start by solving Equation 1 for \( x \):
\[ x = 3y + 18 \]
Next, we can substitute this expression for \( x \) into Equation 2:
\[ 7(3y + 18) - 5y = 46 \]
Now, distribute the 7:
\[ 21y + 126 - 5y = 46 \]
Combine like terms:
\[ (21y - 5y) + 126 = 46 \]
This simplifies to:
\[ 16y + 126 = 46 \]
Now, isolate \( y \) by subtracting 126 from both sides:
\[ 16y = 46 - 126 \] \[ 16y = -80 \]
Now, divide by 16:
\[ y = -5 \]
Now that we have \( y \), we can substitute it back into the equation we derived for \( x \):
\[ x = 3(-5) + 18 \] \[ x = -15 + 18 \] \[ x = 3 \]
The solution to the system of equations is: \[ x = 3, \quad y = -5 \]
Thus, the solution is \((3, -5)\).