Problem
NT-B1-M05-P009 The Equation \(xy=2x+5y\)
#9
★★☆☆☆ Level 2 of 5
Find all positive integer solutions of \(xy=2x+5y\).
Move everything to the left and add \(10\).
We have \(xy-2x-5y=0\), hence \((x-5)(y-2)=10\). The positive divisors of \(10\) are \(1,2,5,10\). Therefore the solutions are \((6,12)\), \((7,7)\), \((10,4)\), \((15,3)\).
The coefficients \(2\) and \(5\) switch places in the factors.