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For what values of $m$ and $n$, does the following pair of linear equations have infinitely many solutions ? $2x + 3y = 7$; $m(x + 2y) + n(x - y) = 21$
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For infinitely many solutions, we have $\frac{2}{m+n} = \frac{3}{2m-n} = \frac{7}{21} = \frac{1}{3} \implies m + n = 6, 2m - n = 9$. Solving the above two equations, we get $m = 5, n = 1$