Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

g180101

  • 2 years ago

4x+5y=13 and 3x+y=-4 using linear combination method

  • This Question is Open
  1. g180101
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i need help

  2. AddemF
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm not sure what you mean by the "linear combination" method, but here's my best guess. View the x coefficients as a vector (4,3) and the y coefficients as a vector (5,1) and likewise the solutions as a vector (13,-4). We want to find some combination of the first two vectors which produces the last. To do that you either have to just think about or turn this into a matrix problem. If you just try thinking about it, you see that you want a negative number in the second coordinate and so you probably want a negative value of x since it has a larger second coordinate. (If this reasoning is opaque I can try to elaborate.) From here we just try stuff. Would x=-3 work? Well, in that case you get -3*(4,3)=(-12,-9) and we want to add some multiple of (5,1) to get (13,-4), but to do that you need y=5 which makes (-12,-9)+(25,5)=(13,-4). So these are the values of x and y. However, that method is sloppy and annoying--better to do this using a matrix \[\left(\begin{matrix}4 & 5 & 13\\ 3 & 1 & -4\end{matrix}\right) \rightarrow \left(\begin{matrix} 1 & 4 & 17 \\3 & 1 & -4\end{matrix}\right)\rightarrow \left(\begin{matrix}1 & 4 & 17 \\ 0 & -11 & -55 \end{matrix}\right)\rightarrow \left(\begin{matrix}1 & 4 & 17\\ 0 & 1 & 5\end{matrix}\right)\] From this last matrix we can see that x+4y=17 and y=5. Therefore x+4(5)=17 and so x=17-20=-3. These are the same values we found the other way.

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

    multiply the 2nd equation by 5, so as to make the numerical value(coefficient) of 'y' same....then subtract equation 2 from one...n we get - 11x = 33.....so x = -3....then substitute the value of 'x' in any of the equations to get the value of 'y'.....

  4. 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.