Problem
NT-B1-M05-P006 The Equation \(7x+11y=1\)
#6
★★☆☆☆ Level 2 of 5
Solve the equation \(7x+11y=1\) in integers.
Find one solution by inspection or by the Euclidean algorithm.
One solution is \(x=-3\), \(y=2\), since \(7(-3)+11\cdot2=1\). All solutions are \(x=-3+11t\), \(y=2-7t\), where \(t\in\mathbb Z\).
Emphasises the link between linear equations and the Euclidean algorithm.