Question

Assertion (A): If x = 2k and y = k − 1 is a solution of 3x − 5y = 7, then k = 2. 

Reason (R): A linear equation in 2 variables has infinitely many solutions.

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true, but R is the incorrect reason for A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

Both A and R are true, but R is the incorrect reason for A.

Explanation:

Assertion (A):

Given:

x = 2k,

y = k − 1,

And the equation:

3x − 5y = 7

Substitute into the equation:

3(2k) − 5(k − 1) = 7

6k − 5k + 5 = 7

k + 5 = 7

∴ k = 2

So, Assertion (A) is True.

But,

The fact that a linear equation has infinitely many solutions is not the reason why k = 2.

We found k = 2 by substituting the expressions for x and y into the equation and solving.

So, R is true, but not the correct explanation for A.