Question

solve by elimination method, a^2x+b^2y=c^2,b^2x+a^2y=d^2

Answer 1

the Given Equations are:
a²x+b²y= c²          ................(1)
b²x+a²y =d²         .................(2)

Multiply eq. 1 by a², eq. 2 by b² and then subtracting 2 from 1

(a⁴-b⁴)x = a²c² - b²d²

$x = \frac{ a^{2}c^{2} - b^{2}d^{2} }{a^{4} - b^{4}}$

Similarly,

$y = \frac{ b^{2}c^{2} - d^{2}a^{2} }{ b^{4} - a^{4}}$

This is the process of Elimination