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UKMT Senior Kangaroo, 2019

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The real numbers $x$ and $y$ satisfy the equations: $xy - x = 180$ and $y + xy = 208$ . Let the two solutions be $(x_1, y_1)$ and $(x_2, y_2)$ . What is the value of $x_1 + 10y_1 + x_2 + 10y_2$ ?

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