Question

Assertion: A linear equation $2x+3y=5$ has a unique solution.

Reason: A linear equation in two variables has infinitely many solutions

Now, choose the correct option.

• A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
• C. If Assertion is correct but Reason is incorrect.
• D. If Assertion is incorrect but Reason is correct.

Answer 1

The correct option is D

If Assertion is incorrect but Reason is correct.

Explanation for the correct option:

Step 1: Explanation for the Assertion

Given equation, $2x+3y=5$

Let's substitute $x=1,y=1$, we get

$$\begin{gathered} \Rightarrow RHS=5 \\ \Rightarrow LHS=2\left(1\right)+3\left(1\right)=5 \\ \Rightarrow LHS=RHS \end{gathered}$$

Thus the point$\left(1,1\right)$ is solution of the equation.

Again if we substitute $x=2.5$ and $y=0$

$$\begin{gathered} \Rightarrow RHS=5 \\ \Rightarrow LHS=2\left(2.5\right)+3\left(0\right)=5 \\ \Rightarrow LHS=RHS \end{gathered}$$

Thus the point $\left(2.5,0\right)$ is solution of the equation also.

Therefore, the equation has infinitely many solutions.

Hence, assertion is incorrect.

Step 2: Explanation for the Reason

As explained with the equation $2x+3y=5$, it was understood that a linear equation with two variables has infinitely many solutions.

Hence it is true that, A linear equation in two variables has infinitely many solutions

Step 3: Checking if assertion and reason are related

Here, assertion is incorrect but reason is correct.

Hence, we conclude the correct answer is option D.