Answer:
a) x = 2, y = 1
b) x = 9, y = -9
Step-by-step explanation:
a) [tex]2^{x+y} = 8[/tex]
⇒ [tex]2^{x+y} = 2^{3}[/tex]
⇒ [tex]x+y = 3[/tex]
and
[tex]3^{2x-y} = 27[/tex]
⇒ [tex]3^{2x-y} = 3^{3\\[/tex]
⇒ [tex]2x-y = 3[/tex]
By solving the above two equations, we get;
x = 2 and y = 1
b) [tex]3^{y+x} = 9^{y+x}[/tex]
⇒ [tex]3^{y+x} = 3^{2y+2x}[/tex]
⇒ [tex]x=-y[/tex]
and
[tex]2^{x-y} = 8^{x-3}[/tex]
⇒ [tex]2^{x-y} = 2^{3x-9}[/tex]
⇒ [tex]2x + y=9[/tex]
By solving the above two equations, we get;
x = 9 and y = -9
