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

Statement 2: On substituting x = 5 and y = 2 in each of the above equation the value of left hand side and right hand side for each equation must be 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.