[tex]\begin{array}{|l} x^{y-2}= 4 \\ x^{2y-3} = 64 \end{array}[/tex]
[tex]\begin{array}{|l} \frac{x^{y}}{x^{2}} = 4 \\ \frac{x^{2y}}{x^{3}} = 64 \end{array}[/tex]
[tex]\begin{array}{|l} (1) x^{y} = 4x^{2} (\text{We raise to the second degree.})\\ (x^{y})^{2} = 64x^{3} \end{array}[/tex]
[tex]\begin{array}{|l} (x^{y})^{2} = 16x^{4} \\ (x^{y})^{2} = 64x^{3} \end{array}[/tex]
16[tex]x^{4}[/tex]=64[tex]x^{3}[/tex] [tex]\Rightarrow[/tex] x=4
We return to (1).
[tex]4^{y}[/tex]=4.[tex]4^{2}[/tex] ; [tex]4^{y}[/tex]=[tex]4^{3}[/tex] ; y=3
(4;3)