Consider the following two statements.

Statement 1: A solution to linear equation 5x - 2y = 1 is x = 3, y = 7.

Statement 2: The linear equation 5x - 2y = 1 has a unique solution.

Which of the following is valid?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and Statement 2 is false.

4. Statement 1 is false, and Statement 2 is true.

If we substitute x = 3 and y = 7 into the equation 5x - 2y = 1, we get

Taking L.H.S.

⇒ 5.(3) - 2.(7)

⇒ 15 - 14

⇒ 1.

Since, L.H.S. = R.H.S.

This confirms that (3, 7) is indeed a solution.

∴ Statement 1 is true.

A single linear equation with two variables (like x and y) represents a line in a coordinate plane.

A line has infinitely many points on it, and each point corresponds to a solution of the equation.

Therefore, a single linear equation has infinitely many solutions, not just one.

∴ Statement 2 is false.

∴ Statement 1 is true, and Statement 2 is false.

Hence, option 3 is the correct option.