Solve the system of equations.

Question

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)

Answer 1

To solve the system of equations:

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

We'll substitute Equation 2 into Equation 1.

First, replace \( x \) in Equation 1 with \( 5y - 1 \):

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

Now, simplify:

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

Combine like terms:

\[ 16y - 2 = -18 \]

Add 2 to both sides:

\[ 16y = -16 \]

Now, divide both sides by 16:

\[ y = -1 \]

Now that we have \( y \), we can substitute it back into Equation 2 to find \( x \):

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

Calculate:

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

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

Therefore, the answer is:

(−6, −1)