Answer:
See below. The solutions are x=-1/3 and y=-4/3
Step-by-step explanation:
[tex]\frac{1}{2}\log_2 y-\log_4 x = 1\\\frac{1}{2}\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\\frac{1}{2}\log_2y = log_44x\\\frac{1}{2}\frac{\log_4y}{\log_4 2}=\log_4 4x\\\log_4y=\log_44x\\4^{\log_4y}=4^{\log_44x}\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -\frac{1}{3}, y=-\frac{4}{3}[/tex]
