Question

Solve the system of equations.
2x+6y=−18
x=5y−1(1 point)
Responses

(−7.25, −1.25)
left parenthesis negative 7.25 comma negative 1.25 right parenthesis

(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

Answer 1

To solve the system of equations:

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

We can substitute the expression for \(x\) from the second equation into the first equation.

Substituting \(x = 5y - 1\) into the first equation:

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

Now, we'll expand and simplify:

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

Combine like terms:

\[
16y - 2 = -18
\]

Next, add 2 to both sides:

\[
16y = -16
\]

Now, divide by 16:

\[
y = -1
\]

Now that we have \(y\), we can find \(x\) using the second equation:

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

Evaluating that gives:

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

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

Thus, the correct answer is:

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