Question

Solve for x and y
a^2x+b^2 y=c^2-eq.1 b^2x+a^2y=d^2-eq.2

Answer 1

multiply eq 1 by b*b.
multiply eq 2 by a*a
and subtract it
you will get your answer

Answer 2

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

And

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

Now we multiply by a2 in equation 1 and by b2in equation 2 and get

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

And

b4 x + a2 b2 y  = b2d2                                                  --- ( 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 a2in equation 2 and get

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

And

a2 b2 x + a4 y  = a2d2                                                   --- ( 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

Therefore,

x = a2c2 − b2d2 a4 − b4  and y = a2d2 − b2c2 a4 − b4