I need to solve these 2 questions:

Question

e^x+2e^y=3

x+y=0

 

and

 

e^x+e^y=e^-2

xy=-15

 

pls haaaalp !

Answer 1

First problem:

 

 solving the second equation for y : y = -x

 

 plugging this into the second equation :  e^x + 2e^-x = 3

 

  Multiplying everything by e^x :

    e^2x + 2 = 3*e^x

 

   e^2x - 3*e^x + 2 = 0   <-- moves 3*e^x to left side

 

  (e^x)^2 - 3*e^x +2 = 0     <--- property of exponents

 

  Z^2 - 3Z + 2 = 0   <---- change variables : let Z = e^x

 

 ( Z      -     2)(Z    -        1)=0    <-- factors

 

 Z - 2 = 0 --> Z = 2  --> e^x = 2  --->  x = ln 2

 

Z - 1 = 0 ---> Z=1 ---> e^x = 1  ---> x = ln 1 = 0

 

so the two solutions are X=ln 2 and X = 0