To solve the system of equations:
- \( x - 3y = 18 \) (Equation 1)
- \( 7x - 5y = 46 \) (Equation 2)
We can solve this using the substitution or elimination method. Here, I’ll use the substitution method.
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 3y + 18 \]
Now, we substitute \( x \) into Equation 2:
\[ 7(3y + 18) - 5y = 46 \]
Expanding this:
\[ 21y + 126 - 5y = 46 \]
Combining like terms:
\[ (21y - 5y) + 126 = 46 \]
\[ 16y + 126 = 46 \]
Now, isolate \( y \):
\[ 16y = 46 - 126 \]
\[ 16y = -80 \]
Dividing by 16:
\[ y = -5 \]
Now that we have \( y \), we can find \( x \) using Equation 1:
\[ x = 3(-5) + 18 \]
\[ x = -15 + 18 \]
\[ x = 3 \]
So the solution to the system of equations is:
\[ (x, y) = (3, -5) \]
Thus, the correct answer is:
(3, −5).