SOLUTION: {{{system((1/2)^(x+y)=16, log(x-y,8)=-3)}}}. Calculate the values of x and y

Let's simplify the equations.

Simplifying the first equation:



Write  as 
And write  as 



Remove the parentheses by multiplying the
inner exponent  by the outer
exponent , getting 



The base on each side is the same
positive number, which is not 1, so
we may equate the exponents:



Let's multiply every term by 



------

Now we simplify the second equation:



Use the rule of logs:   can be rewritten 



Write  as 



Enclose both sides in parentheses and raise to the
 power:



Multiply inner exponents by outer exponents:

 

Write the left side as  and right side as just  



Multiply both sides by 





Put the right side on the left and vice-versa:



------

So we now have this simpler system of equations:



I assume you know how to solve that system.
If you don't, post again asking how:

Answer:  

Edwin