Question

Află x și y numere întregi pentru care xy+2x-3y = 16

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Answer 1

$x(y+2)-3y=16 \\ \\ x=\frac{16+3y}{y+2} \Rightarrow~\left \{ {{(y+2)~|~(y+2)~|*3} \atop {~~(y+2)~|~(3y+16)}} \right. \Leftrightarrow~\left \{ {{(y+2)~|~(3y+6)} \atop {(y+2)~|~(3y+16)}} \right. \Leftrightarrow~(y+2)~|~(3y-3y+16-6)~\Leftrightarrow~y+2\in~D_{10}=\{1,-1,2,-2,5,-5,10,-10\}\\ \\ y=\{-1,-3,0,-4,3,-7,8,-12\}\\ \\ x=\{13,-7,8,-2,5,-1,4,2\}$