To solve the system of equations:
- \( 2x + 6y = -18 \)
- \( x = 5y - 1 \)
We can substitute the expression for \( x \) from the second equation into the first equation.
Substituting \( x = 5y - 1 \) into the first equation:
\[ 2(5y - 1) + 6y = -18 \]
Now simplify this equation:
\[ 10y - 2 + 6y = -18 \]
Combine like terms:
\[ 16y - 2 = -18 \]
Add 2 to both sides:
\[ 16y = -16 \]
Now, divide by 16:
\[ y = -1 \]
Now that we have the value of \( y \), we can substitute it back into the second equation to find \( x \):
\[ x = 5(-1) - 1 \]
\[ x = -5 - 1 \]
\[ x = -6 \]
So the solution to the system of equations is:
\[ (x, y) = (-6, -1) \]
Final answer:
\[ x = -6, \quad y = -1 \]
Thus, the solution is \( (-6, -1) \).
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