A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

7x-8y=40 8y-7x=-40 What is the solution? Consistent or not? Dependent or not?

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

    I think that they are consistent

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

    7 -8 |40 8 -7|-40 //-8/7*R1 + R2 -> R2 7 -8 |40 0 9.14 | -85.7 rank(A) = 2 rank(A|B) = 2 n = 2 so its consistent

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

    so the solution is 2

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

    no, the rank of matrix is 2 so is the system consistent

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

    so can we find out what th solution is and if it is dependent or not

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

    so is the solution infinitely, a point or no solution is my question also

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

    http://en.wikipedia.org/wiki/System_of_linear_equations#Solving_a_linear_system u check the rank of coefficient matrix A and the rank of augmented matrix A|B if (rank(A) == rank(A|B) != col_num of A) there is infinte solutions (parametric solution) if (rank(A) == rank(A|B) == col_num of A) there is one solution if (rank(A) != rank(A|B) ) there is no solution

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

    ok

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

    both your eqns are the same with a sign change. thus, ur system of eqns reduce to only one eqn i.e. either 7x-8y=40 or -7x+8y=-40. thus, we can write 7x=8y+40 which gives x=(8y+40)/7. which means take any value of y and u get the corresponding value of x. Now how many values of y are possible? i assume y is real; hence infinite. thus ur sys of eqn is consistent with infinite solns. Another rule wud be : if a1x+b1y=c1 and a2x+b2y=c2, then if a1/a2=b1/b2=c1/c2 then solns are infinite.

  10. 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.