29. Solve the system of equations:

$$
\left\{\begin{array}{l}
X+\frac{X+2 Y}{X^{2}+Y^{2}}=2 \\
Y+\frac{2 X-Y}{X^{2}+Y^{2}}=0
\end{array}\right.
$$

## 10th grade
79.29. Hint. Consider the sum of the squares of the left-hand sides of the equations. Answer. $X=0, Y=1$ or $X=2, Y=-1$.