Question

which of the following constitutes the solution of the system of equation x+y=2ab and bx/a +ay/b = a²+b²​

Answer 1

solution

You find x and y by solving the two simultaneous equations :

bx/a + ay/b = a^2 + b^2

x + y = 2ab

ab × (i) : b^2 x + a^2 y = ab(a^2 + b^2)………….(iii)

a^2 × (ii) : a^2 x + a^2 y = 2 a^3 b………….(iv)

(iii)-(iv) : (b^2 - a^2)x = ab(a^2 + b^2) - 2a^3 b

(b^2 - a^2)x = ab(a^2 + b^2 - 2a^2) = ab(b^2 - a^2)

x = ab(b^2 - a^2)/(b^2 - a^2)

x = ab.

Subst. x in (ii) : ab + y = 2ab

y = ab.