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:

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

We can substitute the expression for \( x \) from Equation 2 into Equation 1.

Substituting \( x \) in Equation 1:

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

Now, let's distribute in the first term:

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

Combine like terms:

\[
16y - 2 = -18
\]

Now, add 2 to both sides:

\[
16y = -16
\]

Divide by 16:

\[
y = -1
\]

Now that we have \( y \), we can find \( x \) by substituting \( y \) back into Equation 2:

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

So the solution to the system of equations is:

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

Thus, the answer is \((−6, −1)\) which matches the second option in the response choices.