A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
2^x+2^y=10 and 4^x+4^y=68, solve x and y
anonymous
 5 years ago
2^x+2^y=10 and 4^x+4^y=68, solve x and y

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the first equation becomes z+w=10 with that substitution

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now, replace 4 with 2^2, so the second equation becomes 2^2x+2^2y=68 now, 2^2x is that same as 2^x2, which is also the same as (2^x)^2...using a similar argument, for y 4^y is really (2^y)^2 but we called 2^x z and 2^y we called w, so we substitute in and get z^2+w^2=68

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now using the first equation z+w=10, solve for z and then substitute into the second equation. so z=10w and the second equation is then (10w)^2 +w^2=68 expand the (10w)^2 with foil to get 10020w+w^2+w^2=68 and then group like terms and move everything over

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.02w^220w+32=0 dividing out by 2, w^210w+16=0 (w8)(w2)=0 w=2 and w=8 now, plug back in for w=2^y 2^y=2 and 2^y=8...so y=1 and y=3 plugging back in for y=1 gives x=3 and y=3 gives x=1 so the 2 solutions are (1,3) and (3,1)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.