d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by Let (a, b) x = xo + = t, y = Yo - (9) t where t is an arbitrary integer. (1.1)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 43E
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Let (a, b) =d. The linear Diophantine equation ax + by = c has a solution
if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other
solutions are given by
x = xo +
(2) +
t,
y = Yo -
(²) t
where t is an arbitrary integer.
(1.1)
Transcribed Image Text:Let (a, b) =d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any particular solution, that is, axo+byo = c. All other solutions are given by x = xo + (2) + t, y = Yo - (²) t where t is an arbitrary integer. (1.1)
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