Question

why do linear equation have infinite solutions

Answer 1

Hey there !

Solution :

For a single Linear Equation, the values for the variables can be having infinite number of solutions possible.

For Example :

x + y = 100

So x and y can have various values depending on each other's value. Well Infinite here doesn't mean that it is indeterminate. Well actually means that there are countless number of solutions possible for the equation given.

Let's take the above case.

So If we substitute value of x = 1, 2, 3, ..... 50 then the value of y would also be dependent on x by having a value as 49, 48, 47 ..... 1. Here only positive integers are taken into consideration. But if we substitute for negative values also we might get different values which are interdependent. 

Also this can be illustrated in the form of graph. Well refer to the following attachment for the graph.

Well if you notice the graph, the values for x and y keeps on going endlessly on both the directions. This implies that, x and y don't have just a finite number of values but an infinite one.

So We can say that a linear equation can have Infinite Solutions.

Hope my answer helped !

( Attachment 1 - Normal view )
( Attachment 2 - Zoomed out view )

Answer 2

Hi friend, Harish here.

Here is your answer: 

Just few updates from the answer given by @Kalpesh Prabhakar. 

A linear equation does not have infinite solutions always. It is only a valid point for linear equation in two variable. 

For example: 

⇒ x + 1 = 7 

This equation only has one solution, and that is x = 6. 

And in a linear equation with two variable it has infinite solution. But to be specific it actually has infinite Real Solution. 

The Number of positive integral solution are always finite. 

→ The graph attached by @Kalpesh Prabhakar shows that linear equation in two variables have infinite solution. 

→ The graph attached by me shows that some linear equations with one variable has only one solution. 

[NOTE: FOR A SYSTEM OF LINEAR EQUATIONS IN 2 VARIABLE IT MAY NOT HAVE INFINITE SOLUTION]
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Hope my answer is helpful to you.