NT-B1-M05-P001 A Linear Equation

First divide the equation by \(\gcd(4,6)\).

Divide by \(2\): \(2x+3y=5\). One solution is \(x=1\), \(y=1\). Hence all solutions are \(x=1+3t\), \(y=1-2t\), where \(t\in\mathbb Z\). Check: \(2(1+3t)+3(1-2t)=5\).

Basic problem on parametrising integer solutions.