Solve the system of equations.

2x+6y=−18

x=5y−1
(1 point)
Responses

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

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

(5.25, 1.25)

1 answer

To solve the system of equations, we have:

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

We can substitute equation (2) into equation (1).

Substituting \( x \) in equation (1):

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

Distributing the \( 2 \):

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

Combine like terms:

\[ 16y - 2 = -18 \]

Now, add \( 2 \) to both sides:

\[ 16y = -16 \]

Dividing by \( 16 \):

\[ y = -1 \]

Now, substitute \( y = -1 \) back into equation (2) to find \( x \):

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

Thus, the solution to the system of equations is:

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

Therefore, the answer is:

\((-6, -1)\)