Statement 1: x = 5 and y = 2 are the solution of equations x - y = 3 and 2x + y = 11.

Statement 2: x = 5 and y = 2 will be the solutions of the given equations if for each equation, the values on left hand side and right hand side are the same.

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.

Given,

First equation :

⇒ x - y = 3

⇒ x = 3 + y ……..(1)

Second equation :

⇒ 2x + y = 11 ………………….(2)

Substituting the value of x from equation (1) in (2),

⇒ 2(3 + y) + y = 11

⇒ 6 + 2y + y = 11

⇒ 6 + 3y = 11

⇒ 3y = 11 - 6

⇒ 3y = 5

⇒ y = $\dfrac{5}{3}$

Substitute the value of y in equation (1),

⇒ x = 3 + $\dfrac{5}{3}$

⇒ x = $\dfrac{9 + 5}{3}$

⇒ x = $\dfrac{14}{3}$

Thus, x = $\dfrac{5}{3}$ and y = $\dfrac{14}{3}$ are the solution of equations.

So, statement 1 is false.

First equation :

⇒ x - y = 3

Substituting x = 5 and y = 2 in L.H.S. of first equation

⇒ 5 - 2

⇒ 3.

L.H.S. = R.H.S.

Second equation :

⇒ 2x + y = 11

Substituting x = 5 and y = 2 in L.H.S. of second equation

⇒ 2(5) + 2

⇒ 10 + 2

⇒ 12

L.H.S. ≠ R.H.S.

So, statement 2 is false.

∴ Both the statements are false.

Hence, option 2 is the correct option.