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Question 2. Solve the Diophantine equations: (2.a) 21x + 15y = 61 (2.b) 22u + 150 = 6

1 Answer

5 votes

Answer:

no solution (either equation)

Explanation:

2.a 21x +15y = 61 . . . . has no solution in integers

The left side is a multiple of 3; the right side is prime. No multiple of 3 will be a prime number.

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2.b subtracting 6 from both sides and dividing by 2 gives ...

11u +72 = 0

72 is not a multiple of 11, so there can be no integer value of u that satisfies this equation.

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Neither equation has an integer solution.

User Alezis
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