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Question

Solve the system of equations.
2x+6y=−18

x=5y−1
(1 point)
Responses

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

(5.25, 1.25)
left parenthesis 5.25 comma 1.25 right parenthesis

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

(−6, −1)

1 answer

To solve the system of equations:

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

We can substitute the expression for \( x \) from Equation 2 into Equation 1.

Step 1: Substitute Equation 2 into Equation 1.

Substituting \( x = 5y - 1 \) into the first equation:

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

Step 2: Distribute and simplify.

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

Combine like terms:

\[ 16y - 2 = -18 \]

Step 3: Solve for \( y \).

Add 2 to both sides:

\[ 16y = -16 \]

Now divide by 16:

\[ y = -1 \]

Step 4: Substitute \( y \) back into Equation 2 to solve for \( x \).

Using Equation 2:

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

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

So, the solution to the system of equations is:

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

The correct answer from the options given is:

\((-6, -1)\)