Question

Solve the system of equations. 2x+6y=−18 x=5y−1 (1 point) Responses (−6, −1) left parenthesis negative 6 comma negative 1 right parenthesis (−7.25, −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (4, 1) left parenthesis 4 comma 1 right parenthesis (5.25, 1.25)

Answer 1

To solve the system of equations given by:

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

we can substitute the second equation into the first equation.

Starting with the first equation:

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

Substituting \( x = 5y - 1 \):

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

Now, simplify:

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

Combine like terms:

\[
16y - 2 = -18
\]

Add 2 to both sides:

\[
16y = -16
\]

Now, divide by 16:

\[
y = -1
\]

Now, we can find \( x \) using the second equation \( x = 5y - 1 \):

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

\[
x = -5 - 1
\]

\[
x = -6
\]

So, the solution to the system of equations is:

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

The correct answer is:

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