A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

x^2 + xy = 1, xy+y^2 = 3, solve for x and y

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Since you have xy in each equation they must be the same result. Solve the first and second equations for xy

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    xy = 1 - x^2 and xy = 3 - y^2 1 - x^2 = 3 - y^2

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Solve for y: subtract 3 from both sides -2 - x^2 = -y^2 take the opposite of both sides 2 + x^2 = y^2 square root both sides sqrt(x^2 + 2) = y y = sqrt(x^2 + 2)

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Solve for x: 1 - x^2 = 3 - y^2 subtract 1 from both sides -x^2 = 2 - y^2 take the opposite of both sides x^2 = y^2 - 2 square root both sides x = sqrt(y^2 - 2)

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there another way to solve this?

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think the results should be real numbers

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Come on, we can be more elegant than this, guys: Add them both: x^2 + 2xy + y^2 = 4 (x+y)^2 = 4 => x+y = ±2

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Case 1: x = 2-y gives (2-y)y = 3-y^2 => y = 3/2, x = 1/2 Case 2 x = -(2+y) gives -y(2+y) = 3-y^2 gives y = -3/2, x = -1/2

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's how we do it at Cambridge, featheres!

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You're welcome, kiddo.

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x=1/2,x=-1/2 and y=3/2 and y=-3/2 are the answers x(x+y)=1 and y(x+y)=3 implies x/y=1/3 and 3x=y .PLug in this in x^2+xy=1,x^2+3x^2=1,4x^2=1, x^2=1,x=1/2 or -1/2 now we have y3x=3(1/2)=3/2 and -3/2

  13. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.