Solve equations with conjugates multiplications
can we solve x2 and x1 if y2 and y2 are known?

Yes, provided that you mean $y_1$ and $y_2$ are known. If you have two linear equations your can (in most cases) solve for two unknown variables.

If not, can we get the value of y2 based on the equation (1),

No. $y_2$ doesn't show up in equation (1) at all, so you can't get it from there.

which is very similar to equation (1)

Similarity has very little to do with it. You can always solve for two unknown variables unless the two equations are linear dependent. The two that you have are not.