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(a^2 + b^2))/(6(a^2 + b^2))`

`x = 1/2`

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

`6a xx 1/2 + 6by = 3a + 2b`

6by = 2b

`y = (2b)/(6b)`

`y = 1/3`

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