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line solution = infinite solutions

Hey i was told that a line solution implies that there are infinite solutions but i don't see why (even though apparently it's really obvious). I'm completely certain what line solutions are though - could some explain this to me?

thanks in advance :biggrin:
Reply 1
Avatar for Icy_Mikki
Icy_Mikki
13
How many points are there on a line?

Say y = x. Then
(0.1,0.1)
(5,5)
(1000000,1000000)

Are all on the line- in fact, (x,x) is on the line regardless of the value of x. Since there are infinitely many possible values of x, there are infinitely many (x,x)s.
Reply 2
Avatar for Sinay
Sinay
OP
2
Icy_Mikki
How many points are there on a line?

Say y = x. Then
(0.1,0.1)
(5,5)
(1000000,1000000)

Are all on the line- in fact, (x,x) is on the line regardless of the value of x. Since there are infinitely many possible values of x, there are infinitely many (x,x)s.


ohh, lol i've got in the habit of thinking of planes as pieces of paper, so when i think of the line solution of it i think of where the paper stops - so should be thought of as infinitely spanning space, just in a particular orientation?

Surely though that means a plane solution will also give infinite solutions?

thanks for the quick reply
Reply 3
Avatar for LeeC
LeeC
15
Yeh a plane solution should also give infinite solutions!
Reply 4
Avatar for Morbo
Morbo
17
Sinay
ohh, lol i've got in the habit of thinking of planes as pieces of paper, so when i think of the line solution of it i think of where the paper stops - so should be thought of as infinitely spanning space, just in a particular orientation?

Surely though that means a plane solution will also give infinite solutions?

thanks for the quick reply

Even if you were thinking of the intersection of two finite planes in a line segment, there's still infinitely many solutions because the line segment still has infinitely many points.
Reply 5
Avatar for Sinay
Sinay
OP
2
Morbo
Even if you were thinking of the intersection of two finite planes in a line segment, there's still infinitely many solutions because the line segment still has infinitely many points.


yeah that's true actually - lol thanks

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