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
`6a^2x + 6aby = 3a^2 + 2ab`                       ……….(iii)
`6b^2x - 6aby = 3b^2 - 2ab`                         ……….(iv)
On adding (iii) and (iv), we get
`6(a^2 + b^2)x = 3(a^2 + b^2)`
`x =( 3 ( a^2+ b^2))/(6 ( a^2+ b^2)) = 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`.