To solve the system of equations, we have:
- \( 2x + 6y = -18 \)
- \( x = 5y - 1 \)
We can substitute equation (2) into equation (1).
Substituting \( x \) in equation (1):
\[ 2(5y - 1) + 6y = -18 \]
Distributing the \( 2 \):
\[ 10y - 2 + 6y = -18 \]
Combine like terms:
\[ 16y - 2 = -18 \]
Now, add \( 2 \) to both sides:
\[ 16y = -16 \]
Dividing by \( 16 \):
\[ y = -1 \]
Now, substitute \( y = -1 \) back into equation (2) to find \( x \):
\[ x = 5(-1) - 1 \] \[ x = -5 - 1 = -6 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-6, -1) \]
Therefore, the answer is:
\((-6, -1)\)