Question

16. 6x + 5y = 7x + 3y +1 = 2(x + 6y - 1)​

Answer 1

Step-by-step explanation:

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.Read more on Sarthaks.com - https://www.sarthaks.com/130110/solve-for-x-and-y-6x-5y-7x-3y-1-2-x-6y-1