To solve the system of equations given by
- \( x = 6y - 3 \)
- \( 2x + 7y = 13 \)
we will substitute the expression for \( x \) from the first equation into the second equation.
Substituting \( x = 6y - 3 \) into the second equation:
\[ 2(6y - 3) + 7y = 13 \]
Distributing \( 2 \):
\[ 12y - 6 + 7y = 13 \]
Combining the \( y \) terms:
\[ 19y - 6 = 13 \]
Now, add \( 6 \) to both sides:
\[ 19y = 19 \]
Dividing both sides by \( 19 \):
\[ y = 1 \]
Now that we have \( y \), we can find \( x \) using the first equation:
\[ x = 6(1) - 3 = 6 - 3 = 3 \]
So, the solution to the system of equations is \( (x, y) = (3, 1) \).
The final answer is \( (3, 1) \).