Given that `x^2 + y^2 =4` and `x^2 + y^2 -4x -4y` =-4 , then x + y =

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem step by step, we start with the given equations:

1. **Given Equations**:
- \( x^2 + y^2 = 4 \) (Equation 1)
- \( x^2 + y^2 - 4x - 4y = -4 \) (Equation 2)

2. **Substituting Equation 1 into Equation 2**:
From Equation 1, we know that \( x^2 + y^2 = 4 \). We can substitute this value into Equation 2.

\[ 4 - 4x - 4y = -4 \]

3. **Rearranging the Equation**:
Now, we simplify the equation:

\[ -4x - 4y = -4 - 4 \]
\[ -4x - 4y = -8 \]

4. **Factoring Out -4**:
We can factor out -4 from the left side:

\[ -4(x + y) = -8 \]

5. **Dividing Both Sides by -4**:
To isolate \( x + y \), we divide both sides by -4:

\[ x + y = \frac{-8}{-4} \]
\[ x + y = 2 \]

Thus, the final answer is:

\[ \boxed{2} \]