Question #24690

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Answer 1 · 2016-11-22T15:20:20

Considering only positive solutions,

$x=7,y=32$
$x=18,y=17$ and
$x=29, y = 2$

$30x+22y=914$ has the same solutions of

$15x+11y=457$ because $2(15x+11y)=2 cdot457$

$ax+by=c$ has integer solution if and only if $d = gcd(a,b)$ is a divisor of $c$

In our case, $d = 1$ and $c = 457$ is prime, but $1$ is a universal divisor so the equation must have solutions.

$x=7,y=32$
$x=18,y=17$ and
$x=29, y = 2$

Considering only positive solutions.