Question

Solve the system of equations.
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:

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