Problem
NT-B1-M05-P002 Positive Solutions
#2
★☆☆☆☆ Level 1 of 5
Find all positive integer solutions of \(2x+3y=18\).
Look at the parity of \(y\).
From \(2x=18-3y\), the number \(y\) must be even. Since \(y>0\) and \(3y<18\), we have \(y=2\) or \(y=4\). Then \(x=6\) or \(x=3\). The solutions are \((6,2)\), \((3,4)\).
Shows how positivity narrows a linear equation.