Question

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)

Answer 1

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:

\((-6, -1)\)