Question

Solve for x and y:

a²x + b²y = c², b²x + a²y = d²

Answer 1

The given equations are

a²x + b²y = c²    ...(i)

b²x + a²y = d²   ...(ii)

Multiplying (i) by a² and (ii) by b² and subtracting, we get

a⁴x – b⁴x = a²c² – b²d²

⇒ `x = (a^2c^2 - b^2d^2)/(a^4 - b^4)`

Now, multiplying (i) by b² and (ii) by a² and subtracting, we get

b⁴y – a⁴y = b²c² – a²d²

⇒ `y = (b^2c^2 - a^2d^2)/(a^4 - b^4)`

Hence, ` x = (a^2c^2 - b^2d^2)/(a^4 - b^4)` and `y = (b^2c^2 - a^2d^2)/(a^4 - b^4)`.