Question

(i) lf 77x + 63y = 123 and 63x + 77y = 17 then x + y = 5.

(ii) 3x + 2y = 7 and 2x + 3y = 8 gives x = 2, y = 1.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

(i) For the equations 77x + 63y = 123 and 63x + 77y = 17:

If we add these two equations, we get:

(77x + 63y) + (63x + 77y) = 123 + 17

140x + 140y = 140

Dividing by 140, x + y = 1, not 5.

So, (i) is incorrect.

(ii) For the equations 3x + 2y = 7 and 2x + 3y = 8:

Solving by substitution or elimination yields x = 2, y = 1.

So (ii) is correct.

However, since (i) is incorrect and (ii) is correct, the only valid statement is (ii).

Let’s verify (ii) correctly:

3x + 2y = 7

2x + 3y = 8

Multiply the first equation by 3:

9x + 6y = 21

Multiply the second equation by 2:

4x + 6y = 16

Subtract:

(9x + 6y) – (4x + 6y) = 21 – 16

5x = 5

⇒ x = 1

Put x = 1 in 3x + 2y = 7:

3(1) + 2y = 7

⇒ 2y = 4

⇒ y = 2

Therefore, x = 1, y = 2, not x = 2, y = 1, so (ii) is also incorrect.