Question

If `(2x)/3 - y/2 + 1/6 = 0` and `x/2 + (2y)/3 = 3` then

विकल्प

• x = 2, y = 3

• x = –2, y = 3

• x = 2, y = –3

• x = –2, y = –3

Answer 1

x = 2, y = 3

Explanation:

Multiply both equations by 6 to clear denominators (LCM method).

1. `6 xx ((2x)/3 - y/2 + 1/6 = 0)` 

⇒ 4x – 3y + 1 = 0

⇒ 4x – 3y = –1

2. `6 xx (x/2 + (2y)/3 = 3)` 

⇒ 3x + 4y = 18

Solve by elimination:

Multiply (1) by 4: 

16x – 12y = –4

Multiply (2) by 3:

9x + 12y = 54

Add: 25x = 50

⇒ x = 2

Substitute x = 2 into 3x + 4y = 18:

6 + 4y = 18 

⇒ 4y = 12

⇒ y = 3