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Solve the following system of equations algebraically : $73x - 37y = 109$, $37x - 73y = 1$
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Adding and subtracting the given equations, we get $x - y = 1 \dots (i)$ and $x + y = 3 \dots (ii)$. Solving (i) and (ii), we get $x = 2, y = 1$.