Solve for x and y: 6(ax + by) = 3a + 2b, 6(bx – ay) = 3b – 2a

1.	Solve for x and y: 6(ax + by) = 3a + 2b, 6(bx – ay) = 3b – 2a
Answer» 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.

Answer»

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.

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