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2x+6y=−18

x=5y−1
(1 point)
Responses

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

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

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

(5.25, 1.25)

1 answer

To find the solution to the system of equations given by \(2x + 6y = -18\) and \(x = 5y - 1\), we can substitute the second equation into the first equation.

  1. Start by substituting \(x\) in the first equation: \[ 2(5y - 1) + 6y = -18 \]

  2. Distribute \(2\): \[ 10y - 2 + 6y = -18 \]

  3. Combine like terms: \[ 16y - 2 = -18 \]

  4. Add \(2\) to both sides: \[ 16y = -16 \]

  5. Divide by \(16\): \[ y = -1 \]

  6. Now substitute \(y\) back into \(x = 5y - 1\) to find \(x\): \[ x = 5(-1) - 1 = -5 - 1 = -6 \]

So the solution to the system of equations is \((-6, -1)\).

Thus, the correct response is: \[ \text{(−6, −1)} \]