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