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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)

1 answer

To solve the system of equations, we need to substitute the second equation into the first equation.

The equations are:

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

We will substitute the expression for \(x\) from the second equation into the first equation.

Substituting \(x\) in the first equation:

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

Now, distribute the 2:

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

Combine like terms:

\[ 16y - 2 = -18 \]

Next, add 2 to both sides:

\[ 16y = -16 \]

Now, divide by 16:

\[ y = -1 \]

Now that we have \(y\), we can substitute it back into the second equation to find \(x\):

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

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

So, the answer is: \[ \boxed{(-6, -1)} \]