Question

If ax + by = = a² - b² and bx + ay = 0, then the value of x + y is ______.

Options

• a² - b²

• a + b

• a - b

• a² + b²

Answer 1

If ax + by = = a² - b² and bx + ay = 0, then the value of x + y is a - b.

Explanation:

Given:

ax + by = = a² - b²  ...(i)

bx + ay = 0  ...(ii)

Adding equation (i) and (ii)we get,

ax + by + bx + ay = a² - b² + 0

a(x + y) + b(x+y) = a² - b²

(a + b) (x + y) = a² - b²

We recognize that a² − b² is a difference of squares, which can be factored as (a + b)(a − b). So, we have:

(a + b) (x + y) = (a + b) (a - b)

Assuming a + b ≠ 0 (to avoid division by zero), we can divide both sides by (a + b) to isolate x + y:

x + y = a - b

Thus, the value of x + y is a − b.