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Question

Consider the following two statements:

Statement-1: An equation of the form ax+by+c=0, where a,band c are real numbers, such that a,band c are variables and x,y are constants is called linear equation in two variables.

Statement-2: The graph x=a is a straight line parallel to the x-axis.

Which of the following is correct?


A

Statement 1 is true and Statements 2 is false.

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B

Statement 1 is false and Statements 2 is true.

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C

Both statements 1 and 2 are true.

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D

Both statements 1 and 2 are false.

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Solution

The correct option is D

Both statements 1 and 2 are false.


Explanation for the correct option:

Analysing the given two statements:

Let's consider the statement-1,

As we can see ax+by+c=0, involves three variables a,band c so it is called linear equation in three variables.

And hence, the equation of the form ax+by+c=0 cannot be called linear equation in two variables.

Hence, statement-1 is false.

Let's consider the statement-2,

We know that, the graph of x=a is a straight line parallel to y- axis and the graph of y=a is a straight line parallel to x- axis

Here the given statement is, the graph x=a is a straight line parallel to the x-axis.

Therefore, statement-2 is also false.

Hence, we conclude that, since both the statements are false, the correct answer is option D.


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