How do you solve the system $x^{2} - 16 y^{2} = 16$ $x^2-16y^2=16$ and $x^{2} + y^{2} = 9$ $x^2+y^2=9$ ?

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Answer 1 · 2016-08-29T08:51:54

The system of equations don't have real solution.

Making $x_{2} = x^{2}$ $x_2=x^2$ and $y_{2} = y^{2}$ $y_2=y^2$

${(x_2 - 16 y_2 = 16), (x_2 + y_2 = 9):}$

and solving we have

$x_2 = 160/17, y_2=-7/17$

obviously the solution for $y_2$ is not feasible so the system has not real solutions.

How do you solve the system x^2-16y^2=16x2−16y2=16x^2-16y^2=16 and x^2+y^2=9x2+y2=9x^2+y^2=9?