# 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

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