1) 14x + 35y = 91 2) 56x + 72y = 40 3) 24x + 138y...

1) 14x + 35y = 91

2) 56x + 72y = 40

3) 24x + 138y =18

*linear diophantine equations

a) find different solutions for each equation

b) find the value (t), (t) being an arbitrary integer

c) find the general solution for every equation.

d) based on theorem 4.16 give the statement that gives the necessary and sufficient conditions (if and only if) for the equation ax + by = c to have a solution.

(hint) the linear equation ax+by=c has a solution if and only if ______________________________________________.

Expert Solution

Colby Messinger answered 1 year ago

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