Question 70
Compute the unique ordered pair $(x, y)$ of real numbers satisfying the system of equations
$$
\frac{x}{\sqrt{x^{2}+y^{2}}}-\frac{1}{x}=7 \quad \text{ and } \quad \frac{y}{\sqrt{x^{2}+y^{2}}}+\frac{1}{y}=4 .
$$
$$
\frac{x}{\sqrt{x^{2}+y^{2}}}-\frac{1}{x}=7 \quad \text{ and } \quad \frac{y}{\sqrt{x^{2}+y^{2}}}+\frac{1}{y}=4 .
$$