Solve the system of equations.

Question

2x+6y=−18

x=5y−1
(1 point)
Responses

(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis

(−7.25, −1.25)

Answer 1

To solve the system of equations, we'll first substitute the second equation \( x = 5y - 1 \) into the first equation \( 2x + 6y = -18 \).

1. Substitute \( x \) in the first equation: \[ 2(5y - 1) + 6y = -18 \]

2. Distribute the 2: \[ 10y - 2 + 6y = -18 \]

3. Combine like terms: \[ 16y - 2 = -18 \]

4. Add 2 to both sides: \[ 16y = -16 \]

5. Divide by 16: \[ y = -1 \]

Now substitute \( y \) back into the second equation to find \( x \): \[ x = 5(-1) - 1 = -5 - 1 = -6 \]

The solution to the system of equations is \( (x, y) = (-6, -1) \).

Therefore, the correct response is: \[ \text{(−6, −1)} \]