Question

Solve for x and y:

6x + 5y = 7x + 3y + 1 = 2(x + 6y – 1)

Answer 1

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)

x = 3

On substituting x = 3 in (i), we get:

12 – 7y = –2

⇒ 7y = (2 + 12)

⇒ 7y = 14

⇒ y = 2

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