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Solution of a Single Linear Equation in Two Variables

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Question

Find the greatest value of $c$ in order that the equation $7 x + 9 y = c$ may have exactly six solutions in positive integers.

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Solution

The greatest value of $c = (n + 1) a b - a - b = 7 \times 7 \times 9 - 7 - 9 = 425$
Here, $n =$ no of solutions
$a$ and $b$ are coefficents of $x$ and $y$ respectively

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