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:

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