Question

How many solutions are there?
3y-2x = 4 and 4x -6y = -8 ?

Interpret the answer as well.

Answer 1

2 solutions a x and a y

Answer 2

^ Nope, wrong, when I solved I got no solution. Did you solve?

Answer 3

i dont think there wld b a solution to dese pair of eqns.

Answer 4

@Zeerak ...u would hv solved wrong....lol

Answer 5

@fortheloveofscience ^So what should I write?

Answer 6

And what does it mean when we dont have a point of intersection? What does the line represent?

Answer 7

i think you should write no unique solution exists for the pair of equations

Answer 8

a pair of parallel lines..

Answer 9

@fortheloveofscience Thanks, and if we observe, the 2nd equation is just the multiple of the 1st, (x2) with opposite signs, what does it mean?

Answer 10

They're the same equation really. For any (x,(2x+4)/3) in R^2 the equations hold.

Answer 11

oh my gawsh...crap sorry its a pair of coincident lines...

Answer 12

my god..how stupid i can be phew

Answer 13

lol they are the same line, so infinite number of solutions

Answer 14

yeah they are a pair of coincident lines so they have similar solutions...and that too infinite

Answer 15

Infinite number of solutions? What does it mean? I didnt get a single pair of solution when i solved them!

Answer 16

try drawing a graph..ull find urself

Answer 17

No i want to knw in term of solving them algebraically, not graphing

Answer 18

infinite because they overlap at every single point because they are the same graph o.o

Answer 19

okay. I agree to that. But when I solved them I didnt even get a single solution, so how do we conclude algebraically that they have infinite solutions?

Answer 20

okay. I agree to that. But when I solved them algebraically I didnt even get a single solution, so how do we conclude algebraically that they have infinite solutions?

Answer 21

you dont have to solve them because they have the same equation

Answer 22

Eq. 2 => 4x -6y = -8
=> 2x - 3y = -4

Adding Eq.1 and 2:

-2x + 3y = 4
2x + 3y = -4
------------------
0=0

They are not same equations, they have opposite signs.

Answer 23

When you solve two equations, you actually assume one to be true and try to show that the other one is true too. In this case you should find some identity relation. This is a tautology, since for any number, identity is trivially true. So what you assumed should be true, that is, every (x,y) solving the equation you assumed must hold the system of equations.

Answer 24

@IsaacDian Haha, whatever you wrote might be correct. But honestly it was Chinese to me. :D
Don't worry I'll ask my teacher tomorrow the reason. but you get the medal for putting effort to write the answer, which definitely seems geeky.

Thanks.