Find the general solution in positive integers: $5 x - 7 y = 3$

x = 7 p - 5

and

y = 5 p - 4

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x = 4 p - 7

and

y = 8 p - 3

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x = p - 2

and

y = 9 p - 6

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x = p - 15

and

y = 6 - 7 p

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Solution

The correct option is C $x = 7 p - 5$ and $y = 5 p - 4$
Let $y = k$ $\Rightarrow x = \frac{7 k + 3}{5}$

General solution is : $(x, y) = (\frac{7 k + 3}{5}, k)$

Now we will go by options

Let's take 1st option y=5p-4=k

$\Rightarrow x = \frac{7 (5 p - 4) + 3}{5}$

$\Rightarrow x = 7 p - 5$

$∴$ option 'A' is true

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