# Solve for x and y:3(2x + y) = 7xy3(x + 3y) = 11xy x ≠ 1 and y ≠ 1

We have

3(2x + y) = 7xy

And 3(x + 3y) = 11xy

Lets simplify these equations.

3(2x + y) = 7xy

Dividing throughout by xy, and assuming p = 1/x and q = 1/y,

6q + 3p = 7 …(i)

Also, 3(x + 3y) = 11xy

Dividing throughout by xy, and assuming p = 1/x and q = 1/y,

3q + 9p = 11 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Multiply equation (ii) by 2, so that the variable q in both the equations have same coefficient.

Recalling equations (i) and (ii),

6q + 3p = 7

3q + 9p = 11 [×2

- 15p = - 15

p = 1

Substitute p = 1 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(i), we get

6q + 3(1) = 7

6q = 7 – 3

6q = 4

q = 2/3

Thus, p = 1 and q = 2/3

As p = 1

1 = 1/x

x = 1

And q = 1/y,

y = 3/2

Hence, we have x = 1 and y = 3/2

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