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

(−6, −1)
left parenthesis negative 6 comma negative 1 right parenthesis

(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis

(4, 1)

Answer 1

To solve the system of equations, we need to substitute the second equation into the first equation.

The equations are:
1. \(2x + 6y = -18\)
2. \(x = 5y - 1\)

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

Substituting \(x\) in the first equation:

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

Now, distribute the 2:

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

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 substitute it back into the second equation to find \(x\):

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

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

So, the answer is:
\[
\boxed{(-6, -1)}
\]