Question

One number is three times the other number. Write a linear equation in two variables to represent this statement. Also find three solutions of the equation.​

Answer 1

Question:

One number is three times the other number. Write a linear equation in two variables to represent this statement.

Also find three solutions of the equation.

Answer:

(0,0)

(1,3)

(-2,-6)

{ note that we can consider different solutions other than the above solutions , as there are infinitely many solutions for the equation }

Note:

• A linear equation in one variable shows a point on a real number line .

• A linear equation in two variables shows a straight line in two-axes plane.

• A linear equation in three variables shows a plane in space .

• A line contains infinitely many points , thus the equation of the line has infinitely many solutions.

Solution:

Here,

The given statement is ,

" One number is three times the other number."

Let the smaller number be "x" and the greater number be "y".

Thus,

According to the question, we have;

y = 3x (required equation)

Now,

We will get different-different values of "y" for different-different values of "x".

Since , "x" can take place of infinitely many numbers , thus we will have infinitely many values of "y" corresponding to each"x".

And hence, we will have infinitely many solutions of the equation.

Some examples of the solution of the required equation (y = 3x) are:

{ Also, note that the coordinates of the points lying on the line(y = 3x) will be in the form of (a,3a) , where "a" is any arbitrary constant }

If x = 0

Then y = 3•0 = 0

Solution => (0,0)

If x = 1

Then y = 3•1 = 3

Solution => (1,3)

If x = -2

Then y = 3•(-2) = -6

Solution => (-2,-6)

.

.

.

.

.

and many more

Hence,

The solutions for the required equation are : (0,0),(1,3),(-2,-6) ......and so on.