Linear Diophantine equations
General · Mathematics
Study notes
Q: Solve 4x + 6y = 10 in integers. gcd(4,6) = 2, and 2|10: solvable! Divide: 2x + 3y = 5. One solution: x = 1, y = 1 (2+3 = 5 ✓). General: x = 1 + 3t, y = 1 - 2t (b/d = 3, a/d = 2). Check t=1: x=4, y=-1: 16-6 = 10 ✓!