To solve the system of equations:
- \( x = 6y - 3 \) (Equation 1)
- \( 2x + 7y = 13 \) (Equation 2)
We can substitute the expression for \( x \) from Equation 1 into Equation 2.
Substituting \( x \) in Equation 2:
\[ 2(6y - 3) + 7y = 13 \]
Now, simplify the left-hand side:
\[ 12y - 6 + 7y = 13 \]
Combine like terms:
\[ 19y - 6 = 13 \]
Next, add 6 to both sides:
\[ 19y = 19 \]
Now, divide by 19:
\[ y = 1 \]
Now that we have \( y \), we can find \( x \) using Equation 1:
\[ x = 6(1) - 3 \] \[ x = 6 - 3 \] \[ x = 3 \]
Thus, the solution to the system of equations is:
\[ \boxed{(3, 1)} \]