To solve the system of equations
- \( 8x - 4y = -28 \)
- \( 2x - 6y = 8 \)
we can use the substitution or elimination method. Let's use the elimination method.
First, simplify the equations if possible.
For the first equation, divide all terms by 4:
\[ 2x - y = -7 \quad \text{(Equation 1)} \]
For the second equation, leave it as is or divide it by 2:
\[ x - 3y = 4 \quad \text{(Equation 2)} \]
Now, we have the simplified system:
- \( 2x - y = -7 \)
- \( x - 3y = 4 \)
Next, we can express \( y \) in terms of \( x \) from Equation 1:
\[ y = 2x + 7 \]
Now substitute this expression for \( y \) into Equation 2:
\[ x - 3(2x + 7) = 4 \]
This simplifies to:
\[ x - 6x - 21 = 4 \] \[ -5x - 21 = 4 \] \[ -5x = 4 + 21 \] \[ -5x = 25 \] \[ x = -5 \]
Now that we have \( x \), substitute back to find \( y \):
\[ y = 2(-5) + 7 \] \[ y = -10 + 7 \] \[ y = -3 \]
Thus, the solution is \( (x, y) = (-5, -3) \).
The solution to the system of equations is:
\[ \boxed{(-5, -3)} \]
So the correct response from the options provided is \( \text{(−5,−3)} \).