Question

Solve the 2 equations and find values of x and y:​

Answer 1

x/a + y/b = a + b

x/a^2 + y/b^2 = 2

multiplying the first equation by a and second equation by a^2 and subtracting we get

x + (a/b)y = a(a + b)

x + (a/b)^2 y = 2a^2

-. -. -

--------------------------------

((a/b) - (a/b)^2) y = a^2 + ab - 2a^2

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

multiplying both side by b^2 we get

(ab - a^2) y = b^2(ab - a^2)

y = b^2

now

x/a^2 + y/b^2 = 2

x /a^2 + b^2/b^2 = 2

x /a^2 + 1 = 2

x/a^2 = 2 - 1 = 1

x = a^2

thus,

x = a^2

y = b^2