Solve for x and y:
6x + 5y = 7x + 3y + 1 = 2(x + 6y - 1)
Since, if a = b = c ⇒ a = b & b = c
Thus, we have
6x + 5y = 7x + 3y + 1
2(x + 6y – 1) = 7x + 3y + 1
Lets simplify these equations. We can rewrite them,
6x + 5y = 7x + 3y + 1
⇒ 7x – 6x + 3y – 5y = - 1
⇒ x – 2y = - 1 …(i)
2(x + 6y – 1) = 7x + 3y + 1
⇒ 2x + 12y – 2 = 7x + 3y + 1
⇒ 7x – 2x + 3y – 12y = - 2 – 1
⇒ 5x – 9y = - 3 …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply eq.(i) by 5, so that variable x in both the equations have same coefficient.
Recalling equations (i) & (ii),
x – 2y = - 1 [×5
5x – 9y = - 3
⇒ - y = - 2
⇒ y = 2
Substitute y = 2 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
x – 2(2) = - 1
⇒ x – 4 = - 1
⇒ x = - 1 + 4
⇒ x = 3
Hence, we have x = 3 and y = 2