Question

If ax + by = a ^2 - b^2 and bx + ay = 0 then find the value of x + y
​

Answer 1

$ax + by = {a}^{2} - {b}^{2} \\ bx + ay = 0 \\ \\ adding \: both \: the \: equations \: we \: get \\ \\ ax + bx + ay + by = {a}^{2} - {b}^{2} \\ (a + b)x + (a + b)y = (a + b)(a - b) \\ \\ dividing \: throughout \: by \: a + b \: we \: get \\ \\ x + y = a - b$

Hence,

x + y = a - b