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Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The numbers $x$ and $y$ satisfy the equations: $xy = \frac{7}{6}$ , $x(y+1) = \frac{5}{3}$ , $y(x+1) = \frac{7}{2}$ . What is the value of $(x+1)(y+1)$ ?

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