Question

A^2x+b^2y=c^2
b^2x+a^2y=d^2

Answer 1

Step-by-step explanation:

We have equations :

a2 x + b2 y = c2 --- ( 1 )

And

b2 x + a2 y = d2 --- ( 2 )

Now we multiply by a2 in equation 1 and by b2 in equation 2 and get

a4 x + a2 b2 y = a2c2 --- ( 3 )

And

b4 x + a2 b2 y = b2 d2 --- ( 4 )

Now we subtract equation 4 from equation 3 and get

a4 x - b4 x= a2c2 - b2 d2

( a4 - b4 ) x= a2c2 - b2 d2

x = a2c2 − b2d2 a4 − b4

And we multiply by b2 in equation 1 and by a2 in equation 2 and get

a2 b2 x + b4 y = b2c2 --- ( 5 )

And

a2 b2 x + a4 y = a2 d2 --- ( 6 )

Now we subtract equation 5 from equation 6 and get

a4 y - b4 y= a2d2 - b2 c2

( a4 - b4 ) y = a2d2 - b2 c2

y = a2d2 − b2c2 a4 − b4