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using geometry? maybe you mean using purely algebra?

ya solving equations... algebra is ok.. . :)

just set y1 = 2y2
make substitutions and solve for x

it's not that simple lol..try it

i mean two values of x

ok leme try
3x/7 = 4x/7 + 686
yes it gives -ve x
it has no +ve solution i'd guess..

no positive values only -4802

|dw:1340005766066:dw|

humm.. lets say x axis is time

at t=0, y2 is 343 more than y1

just enter the equation y1=2*(y2) and you'll see that there is only one value which is -4802.

since y1 is increasing much faster than y2, at some point y1 reaches y2

after some more time, y1 value reaches double the y2 also right ?

are you sure you entered the correct equations?

there should be two values for x.. goes from \[-\infty \to + \infty\]

i am going for lunch.. brb

sure there must be some explanation...

maybe k is ratio of magnitudes by default,, :|

Much later..
I sketched the graph. It's clear that the two lines must cross. Since the relative slope (y1 grows faster than y2) is 1/7, that happens at 7 (343) = x = 2401. There, y1 = 3 (343) and y2 = 2 (343) + 343 = 1029.
However, since y2 is moving away from the x-axis with a slope of 2/7, and y1 only grows faster than y2 by 1/7, I think there is no way y1 can ever be twice y2.
Instead, at any x > 2401, (I think) y2 will be 2/3 of the way to y1 up from 1029. HTH.

yw