2^x + 2^y = 12
x + y = 5
How do you solve this algebraically (instead of guess and check)?

Question

2^x + 2^y = 12
x + y = 5
How do you solve this algebraically (instead of guess and check)?

anonymous · Answer

frome second equation we have y=5-x plug this into first one and solve for x

anonymous · Answer

i got 2^5 = 12 which is a false statement...
2^x + 2^y = 12
x + y = 5

y = 5 - x
2^x + 2^5 - x = 12
2^x + 5 - x = 12
2^5 = 12
2^5 = 32
32 does not equal 12...

anonymous · Answer

dude what did u do ??

anonymous · Answer

i substituted y = 5^x in the first equation, making that part of the equatoin 2^5 - x

anonymous · Answer

after sub we have$$2^x+2^{5-x}=12$$

anonymous · Answer

$$2^x+\frac{2^5}{2^x}=12$$let $$z=2^x$$$$z+\frac{32}{z}=12$$multiply by z$$z^2-12z+32=0$$this is a quadratic solve for z and ...

anonymous · Answer

oh i got it before i was using a rule for simplifying exponents (n^y x n^z = n^y = z) incorrectly, i was using it with addition which doesn't work. Thank you!

anonymous · Answer

no problem