Question

Question
Solve the system of equations.
2x+6y=−18

x=5y−1
(1 point)
Responses

(4, 1)
left parenthesis 4 comma 1 right parenthesis

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

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

(−6, −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.

**Step 1: Substitute Equation 2 into Equation 1.**

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

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

**Step 2: Distribute and simplify.**

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

Combine like terms:

\[
16y - 2 = -18
\]

**Step 3: Solve for \( y \).**

Add 2 to both sides:

\[
16y = -16
\]

Now divide by 16:

\[
y = -1
\]

**Step 4: Substitute \( y \) back into Equation 2 to solve for \( x \).**

Using Equation 2:

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

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

So, the solution to the system of equations is:

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

The correct answer from the options given is:

\((-6, -1)\)