To solve the system of equations:
- \(-4x - y = -28\) (Equation 1)
- \(x + y = 4\) (Equation 2)
We can use the substitution or elimination method. Here, I'll use substitution. First, we can solve Equation 2 for \(y\):
\[ y = 4 - x \]
Now we can substitute this expression for \(y\) into Equation 1:
\[ -4x - (4 - x) = -28 \]
Now, simplify this equation:
\[ -4x - 4 + x = -28 \]
Combine like terms:
\[ -3x - 4 = -28 \]
Next, add 4 to both sides:
\[ -3x = -24 \]
Now, divide by -3:
\[ x = 8 \]
Now that we have \(x\), we can find \(y\) using Equation 2:
\[ y = 4 - x = 4 - 8 = -4 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (8, -4) \]
To verify, we can substitute \(x = 8\) and \(y = -4\) back into both original equations:
- For Equation 1:
\[ -4(8) - (-4) = -32 + 4 = -28 \quad \text{(True)} \]
- For Equation 2:
\[ 8 + (-4) = 4 \quad \text{(True)} \]
Since both equations hold true, the solution is confirmed as:
\[ \boxed{(8, -4)} \]