Solve for x and y in the equations below x2 - y2 = 4 x + y = 2

Analyze the question: We have two equations: x² − y² = 4 and x + y = 2. We need the values of x and y that satisfy both.

Concept: Difference of two squares: x² − y² = (x + y)(x − y). This lets us use the second equation directly.

Solution:

1. Factorise the first equation: (x + y)(x − y) = 4

2. Substitute x + y = 2: 2(x − y) = 4 x − y = 2

3. Now solve the pair: x + y = 2 x − y = 2

Add them: 2x = 4, so x = 2. Then y = 2 − 2 = 0.

4. Check in the original equations: • x² − y² = 4 − 0 = 4 ✓ • x + y = 2 + 0 = 2 ✓

Checking the other options:

• A: x + y = −2 ✗
• B: x² − y² = −4 ✗
• D: x + y = −2 ✗

Answer: x = 2, y = 0, which is option C.

Tip: Whenever you see x² − y² alongside x + y (or x − y), factorise immediately. It turns a quadratic-looking system into two simple linear equations. In multiple choice, you can also quickly test the options in the simpler equation (x + y = 2) to eliminate wrong ones fast.