To solve the system of equations, we have:
- \( 2x + 6y = -18 \) (Equation 1)
- \( x = 5y - 1 \) (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 \((-6, -1)\).