OK, but since one line had sqrt(2y) and the next line has it as sqrt(2)*y there must be a problem with what you wrote.2y is under the radical. Sorry for the confusion.
Thank you for your help! It worked well! Thank you.Make a substitution [imath]u = \dfrac{x}{y}[/imath]
[math]\tag{1}4^u+3\times4^{5-u}=16[/math][math]\tag{2}\sqrt{u}+\sqrt{2}= \dfrac{\sqrt{12}-\sqrt{8}}{\sqrt{y}}[/math]
You can solve for [imath]u[/imath] from equation (1) and use equation (2) to solve for [imath]y[/imath], then [imath]x[/imath] follows.
Please share your solution - so that it can teach other students.Thank you for your help! It worked well! Thank you.