Question

Solve for x and y: 

6(ax + by) = 3a + 2b, 

6(bx – ay) = 3b – 2a

Answer 1

The given equations are 

6(ax + by) = 3a + 2b 

⇒6ax + 6by = 3a + 2b ………(i) 

and 6(bx – ay) = 3b – 2a 

⇒6bx – 6ay = 3b – 2a ………(ii) 

On multiplying (i) by a and (ii) by b, we get 

6a²x + 6aby = 3a² + 2ab ……….(iii) 

6b²x - 6aby = 3b² - 2ab ……….(iv) 

On adding (iii) and (iv), we get 

6(a² + b²)x = 3(a² + b²)

x = 3(a²+ b²)/6(a²+b²) = 1/2

On substituting x = 1/2 in (i), we get: 

6a × 1/2 + 6by = 3a + 2b 

6by = 2b 

y = 2b/6b = 1/3 

Hence, the required solution is x = 1/2 and y = 1/3.