Question

How do you tell if a problem has one solution, many, or none?

Answer 1

I have 4 math problems that I have to figure out if they are either 1) has no solution 2) has infinantely many solutions or 3) has one solution without graphing the problems. Has anyone ever heard of this concept in Algebra?

here's number 1.

y=2x AND

y=-2x-5
_________


number 2.

x+y=4 AND

2x+2y=8

________

Here's number 3.

y=-3x+1 AND

y=3x+7

_______

And finally, number 4.

3x-5y=0 AND

y=3/5(fraction)x

Answer 2

so if you answer this you will side by side get to your answer too.

Answer 3

wow thanks!

Answer 4

It is a memorization thing.

Solve the System any way you like.

If you get something like this: x = 5 and y = 3/2, that is one solution and it is unique. This is an Independent, Consistent System.

If you get something like this: 0 = 4, that is silly and not a solution at all. This is an Inconsistent System.

If you get something like this: 6 = 6, that is a little too obvious and doesn't care about your variables. This is infinitely many solutions, since you can pick any value you like for x.. This is a Dependednt, Consistent System.

Recap!

Just 1 -- x = 9 and y = 4/3
None -- 16 = 7
Infinitely Many -- \(\sqrt{2} = \sqrt{2}\)