Please help me to Solved the simultaneous equation x^2 + y^2 = 10........(1), 1/x + 1/ y = 4/3.....(1)

Answer 1

With the help of a calculator, I found four solutions:

x = 1 , y =3

x = 3 y = 1

x = -3.1 y = .604 ( approx)

x = .604 y = -3.1 (approx)

My method of solution was to change to polar coordinates

x = r cos(θ) y = r sin(θ)

From the first equation r = sqrt(10)

The second equation is then 1/cos(θ) + 1/sin(θ) = (4/3) sqrt(10)

This equation in one variable, can be explored with the help of a a graphing calculator to find the solutions for θ and then to get x and y.

Answer 2

On inspection the rational solutions are (3, 1) and (1, 3).

Elimination or substitution do not work because of an xy term.

I do not know of an Algebra 2 solution.