Question

Consider the following three statements:

Statement- $1$: A linear equation in two variables has only two solutions.

Statement - $2$ : The graph of every linear equation in two variables is a straight line.

Statement- $3$: $x=0$ is the equation of $x$-axis.

Which of the following is correct?

• A. Statement$1$is true and Statements $2$ and $3$ are false.
• B. Statement $2$ is true and Statements $1$ and $3$ are false.
• C. Statement $3$ is true and Statements $1$ and $2$ are false.
• D. All the Statements are true.

Answer 1

The correct option is B

Statement $2$ is true and Statements $1$ and $3$ are false.

Explanation for the correct option:

Step 1: Analysing the statement - $1$

Statement -$1$: A linear equation in two variables has only two solutions.

Every point of the line be the solution of their corresponding linear equation so it has infinitely many solutions.

Hence Statement -$1$ is false.

Step 2: Analysing the statement - $2$

Statement -$2$: The graph of every linear equation in two variables is a straight line

Every linear equation in two variable is represented as $y=mx+c$, where $c$ is constant and $m$ is slope of the line.

We know that $y=mx+c$represents straight line.

Hence statement -$2$ is true.

Step 3: Analysing the statement - $3$

Statement -$3$: $x=0$ is the equation of $x$-axis.

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

Therefore, the graph of equation $x=0$ will be $y$ axis itself.

Therefore statement -$3$ is false.

Hence we conclude the correct answer is option B.