Thayaden 06.05.2022 18:49 Rukevwe wrote: Find all integer solutions of the equation $xy+5x-3y=27$. Simon factor tick states: $$xy+jx+ky=n$$$$(x+k)(y+j)=n+jk$$see if this applies to your equation
iniffur 06.05.2022 22:57 $xy+5x-3y=27\Longrightarrow x=\frac{3y+27}{y+5}=\frac{3y+15+12}{y+5}=3+\frac{12}{y+5}$, $\mid y+5 \mid\le12$ $\Longrightarrow y+5 \in$ {$-12,-6,-4,-3,-2,-1,1,2,3,4,6,12$} $\Rightarrow (x,y)=(2,-17),(1,-11),(0,-9),(-1,-8),(-3,-7),(-9,-6),(15,-4),(9,-3),(7,-2),(6,-1),(5,1),(4,7)$