To solve the system of equations, we have:
1. \( 2x + 6y = -18 \) (Equation 1)
2. \( x = 5y - 1 \) (Equation 2)
We'll substitute Equation 2 into Equation 1.
Substituting \( x \) in Equation 1:
\[
2(5y - 1) + 6y = -18
\]
Now, distribute the 2:
\[
10y - 2 + 6y = -18
\]
Combine like terms:
\[
16y - 2 = -18
\]
Add 2 to both sides:
\[
16y = -16
\]
Now divide by 16:
\[
y = -1
\]
Next, substitute \( y \) back into Equation 2 to find \( x \):
\[
x = 5(-1) - 1 = -5 - 1 = -6
\]
So the solution to the system of equations is:
\[
(x, y) = (-6, -1)
\]
Now we will compare our results with the provided options:
- (5.25, 1.25)
- (−7.25, −1.25)
- (4, 1)
- (−6, −1)
The correct solution is \((-6, -1)\).