Equations

Hairsy

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Oct 23, 2013
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Hello, I need some help with this problem:

Find all vectors (a,b) for which the solution of these equations is multiple of (a,b)

x + y = a
2x + 4y = b

(I hope I wrote it right. X must be k*a and Y k*b). Thank you for help!
 
Hello, I need some help with this problem:

Find all vectors (a,b) for which the solution of these equations is multiple of (a,b)

x + y = a
2x + 4y = b

(I hope I wrote it right. X must be k*a and Y k*b). Thank you for help!
Proceed with the solution of the given system. What method should you use? Will matrix notation be helpful? We need to see your work to know what tools you have, and where you are getting stuck.

EDIT: Do you know about eigenvalues and eigenvectors?
 
Last edited:
Hello, I need some help with this problem:

Find all vectors (a,b) for which the solution of these equations is multiple of (a,b)

x + y = a
2x + 4y = b
Multiply the first equation by 2 to get 2x+ 2y= 2a. Do you see that subtracting from the second equation eliminates x? That allows you to solve for x. If you multiply the first equation by 4 you get 4x+ 4y= 4a and that allows you to eliminate y and solve for x. Once you have the solutions, in terms of a and b, you should be able to find values of a and b that make the solution a multiple (a, b)
(I hope I wrote it right. X must be k*a and Y k*b). Thank you for help!
 
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