Solve the system of equations.

Question

8x−4y=−28

2x−6y=8
(1 point)
Responses

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

(−5,−3)
left parenthesis negative 5 comma negative 3 right parenthesis

(7, 1)
left parenthesis 7 comma 1 right parenthesis

(−2, 3)

Answer 1

To solve the system of equations:

1. \( 8x - 4y = -28 \) (Equation 1)
2. \( 2x - 6y = 8 \) (Equation 2)

Let's solve it step by step.

Step 1: Simplify both equations if possible.

Equation 1: \[ 8x - 4y = -28 \] Divide the entire equation by 4: \[ 2x - y = -7 \] (Equation 3)

Equation 2: \[ 2x - 6y = 8 \] Divide the entire equation by 2: \[ x - 3y = 4 \] (Equation 4)

Now we have the simplified system:

1. \( 2x - y = -7 \) (Equation 3)
2. \( x - 3y = 4 \) (Equation 4)

Step 2: Solve one of the equations for one variable. Let's solve Equation 4 for \( x \): \[ x = 3y + 4 \]

Step 3: Substitute \( x \) in Equation 3: \[ 2(3y + 4) - y = -7 \] \[ 6y + 8 - y = -7 \] \[ 5y + 8 = -7 \] Subtract 8 from both sides: \[ 5y = -15 \] Divide by 5: \[ y = -3 \]

Step 4: Substitute \( y \) back into the equation for \( x \): \[ x = 3(-3) + 4 \] \[ x = -9 + 4 \] \[ x = -5 \]

Thus, the solution to the system is: \[ (x, y) = (-5, -3) \]

The correct answer is: (−5,−3).