Answer to Question #74538 in Algebra for Rajni

Question #74538

Find x and y , given that (5x+y,3x-y) = (2,2x) belong to Q*Q?

Expert's answer

If (5x+y, 3x-y)=(2,2х)
Then
5x+y=2 (1) and 3x-y=2x (2)
Solving (2):
3x-y=2x
3x-2x=y
x=y
Given x=y we can substitute y for x in (1):
5x+x=2
6x=2
x=2/6=1/3
As x=y => x=y=1/3
Answer:
(1/3,1/3)

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