Question

Solve for x and y:
`a^2x + b^2y = c^2, b^2x + a^2y = d^2`

Answer 1

The given equations are
`a^2x + b^2y = c^2`            ………(i)
`b^2x + a^2y = d^2`             ………(ii)
Multiplying (i) by `a^2 and (ii)  by   b^2` and subtracting, we get
`a^4x – b^4x = a^2c^2 - b^2 d^2`
`⇒x = (a^2c^2−b^2d^2)/ (a^4− b^4)`
Now, multiplying (i) by `b^2` and (ii) by `a^2` and subtracting, we get
`b^4y – a^4y = b^2c2 - a^2 d^2`
`⇒y =(b^2 c^2−a^2d^2)/ (b^4− a^4)`
Hence,` x = (a^2c^2−b^2d^2)/( a^4− b^4) and y = (b^2c^2−a^2d^2)/(b^4− a^4)`.