Exponential system of equations

ifrogot1:

2^x+2^y=10
x+y=4
How do I solve this system of equations?

x+y=4 --> y=4-x

2 ^x + 2 ^y = 10 sub in 4-x for y

2 ^x + 2 ^4-x = 10

2 ^x + 2 ⁴/2 ^x = 10

Multiply both sides by 2 ^x

2 ^x2 ^x + 2 ⁴ = 10*2 ^x

(2 ^x) ² - 10*2 ^x + 16 = 0

Let g=2 ^x

g ² - 10g + 16 = 0

So i need 2 numbers that multply to +16 and add to -10
They are -8 and -2 so

(g-8)(g-2)=0
g=8 or g=2

8=2 ^x or 2=2 ^x
2 ³=2 ^x or 2 ¹=2 ^x
x=3 or x=1
now y=4-x
so
x=3, y=1 OR x=1. y=3
solutions are (3,1) or (1,3)

check
http://www.wolframalpha.com/input/?i=2%5Ex%2B2%5Ey%3D10%2C+x%2By%3D4