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Roots of Quadratic Equation

Solve in posi...

Question

Solve in positive integers:
$3 x + 3 x y - 4 y = 14$ .

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Solution

$3 x + 3 x y - 4 y = 14$

Taking $x = 3$
$9 + 9 y - 4 y = 14$
$5 y = 5$
$⟹ y = 1$

Taking $x = 2$
$6 + 6 y - 4 y = 14$
$2 y = 8$
$⟹ y = 4$

$∴$ Solution is $x = 3, 2; y = 1, 4$

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