Solve for x and y if x - y = 2 and x2 - y2 = 8

Analyze the question: We have two equations: x - y = 2 and x² - y² = 8 (the "x2 - y2" is x² - y²). We need the pair (x, y) that satisfies both.

Concept: Use the difference of two squares: x² - y² = (x - y)(x + y)

Solution:

1. Substitute x - y = 2 into the factorised form: (x - y)(x + y) = 8 2(x + y) = 8 x + y = 4

2. Now solve the pair of simultaneous equations: x - y = 2 x + y = 4

3. Add them: 2x = 6, so x = 3.

4. Substitute back: 3 + y = 4, so y = 1.

Check:

• x - y = 3 - 1 = 2 ✓
• x² - y² = 9 - 1 = 8 ✓

Checking the other options quickly:

• A (-1, 3): -1 - 3 = -4 ✗
• C (-3, 1): -3 - 1 = -4 ✗
• D (1, 3): 1 - 3 = -2 ✗

Answer: B. (3, 1)

Tip: Whenever you see x² - y² together with x - y (or x + y), immediately factorise as (x - y)(x + y). It turns a quadratic-looking problem into a simple linear one. You can also test the options quickly with the first equation, x - y = 2, which eliminates A, C and D right away.