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 have:

1. \( 2x + 6y = -18 \) (Equation 1)
2. \( x = 5y - 1 \) (Equation 2)

We can substitute Equation 2 into Equation 1.

First, replace \( x \) in Equation 1 with \( 5y - 1 \):

\[ 2(5y - 1) + 6y = -18 \]

Now simplify:

\[ 10y - 2 + 6y = -18 \]

Combine like terms:

\[ 16y - 2 = -18 \]

Now, add 2 to both sides:

\[ 16y = -16 \]

Divide both sides by 16:

\[ y = -1 \]

Now that we have \( y \), we can find \( x \) using Equation 2:

\[ x = 5(-1) - 1 \] \[ x = -5 - 1 \] \[ x = -6 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (-6, -1) \]

The correct answer is:

\[ \boxed{(-6, -1)} \]