The given equations are:
6x + 5y = 7x + 3y + 1 = 2(x + 6y – 1)
⇒6x + 5y = 2(x + 6y – 1)
⇒6x + 5y = 2x + 12y – 2
⇒6x – 2x + 5y – 12y = -2
⇒4x – 7y = -2 …….(i)
and 7x + 3y + 1 = 2(x + 6y – 1)
⇒7x + 3y + 1 = 2x + 12y – 2
⇒7x – 2x + 3y – 12y = -2 – 1
⇒5x – 9y = -3 …….(ii)
On multiplying (i) by 9 and (ii) by 7, we get:
36x - 63y = -18 ……(iii)
35x - 63y = -21 ……(iv)
On subtracting (iv) from (iii), we get:
x = (-18 + 21) = 3
On substituting x = 3 in (i), we get:
12 - 7y = -2
⇒7y = (2 + 12) = 14
⇒y = 2
Hence, the solution is x = 3 and y = 2.
