Multiple Equations

[Strongt]

Hi everyone,

this is my 1st post, so I'm not sure if this is the right place to ask

I just want to know the difference between equations that has infinite number of solutions and equations that has only 1 solution?

how can i distinguish between the two

Thanks

[vineeshp]

An equation in which the variable takes only value is an equation with 1 solution.

for example 3x = 15 .
Here x takes only one value x=5.

Infinite: In this case, where the equation can take infinite values and still hold good.
For example, 3x + 4 y = 15. You can find infinite values for x , y.
If x = 1, y= 3
x = 3, y = 1.5
And so on.
You wont have to worry about such equations on the GMAT.

[Ian Stewart]

Hi everyone,

this is my 1st post, so I'm not sure if this is the right place to ask

I just want to know the difference between equations that has infinite number of solutions and equations that has only 1 solution?

how can i distinguish between the two

Thanks

That's a really vast question with no straightforward answer, since there are so many possible types of equation you might see on the GMAT. In short, there are no universal rules except in very simple situations. I've posted at length about equations and solutions a few times -- for example, here:

www.beatthegmat.com/n-variables-n-disti ... 20728.html

and hopefully that clarifies a few things. Even when you limit yourself to single equations with one unknown, there are many possible situations. A simple equation like the following:

2x -3 = 5x + 9

will have just one solution for x, but if you introduce exponents you can have two solutions:

x^2 = 4

for example has the solutions x = 2 and x = -2. And it is also possible to have an infinite number of solutions; the equation

x = x

for example is obviously true for any number at all, and it's easy to produce many other 'vacuous' equations with an infinite number of solutions, like x^0 = 1, or x^3 = x*x*x.