Solving the system $XA_k+ YB_k+ XYC_k+ \overline{X}D_k + Y\overline{X}E_k+X\overline{X}F_k+XY\overline{X}G_k+H_k=0$ with $k=1,2$ for complex $X, Y$

Question

Unknowns are two, which are complex numbers $X$ and $Y$ with $|X|<1$ and $|Y|<1$. Remaining values are complex constants.

$$\begin{align} XA_1+ YB_1+ XYC_1+ \overline{X}D_1 + Y\overline{X}E_1 + X\overline{X}F_1 + XY\overline{X}G_1+ H_1 &= 0 \tag1\\ XA_2+ YB_2+ XYC_2+ \overline{Y}D_2 + X\overline{Y}E_2 + Y\overline{Y}F_2 + XY\overline{Y}G_2+ H_2&= 0 \tag2 \end{align}$$

where $\overline{z}$ is the complex conjugate of $z$.

How to solve for the two unknowns when the equations contain the complex conjugate?