Linear Diophantine Equations Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for  

(2) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for

(3) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for  

(4) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for

(5) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for

(6) A grocer order apples and oranges at a total cost of If apples cost him each and oranges cost him each, how many of each type of fruit did he order?

(7) A postal clerk has only and stamps to sell. What combination of these may be used to mail a package requiring postage of exactly

(8) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for

(9) Solve the linear Diophantine equation by either finding all solutions or by showing there are none for

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