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Solve the following Diophantine equation. 25x + 13y = 2

Solve the following Diophantine equation. 25x + 13y = 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer question 9 with details on how to do it. Thank you.

8. Solve the following congruences. a. 5x + 3 = 13 (mod 14) b. 4x = 20 (mod 8) 9. Solve the following Diophantine equation. 25x + 13y = 2 10. A small clothing manufacturer produces two styles of sweaters: cardigan and pullover. She sells cardigans for $25 each and pullovers for $19 each. If her total revenue from a day's production is $1492, how many of each type might she manufacture in a day? There may be multiple answers, so show the general form with k E Z and then pick different values for k to generate some possible answers.
Transcribed Image Text:8. Solve the following congruences. a. 5x + 3 = 13 (mod 14) b. 4x = 20 (mod 8) 9. Solve the following Diophantine equation. 25x + 13y = 2 10. A small clothing manufacturer produces two styles of sweaters: cardigan and pullover. She sells cardigans for $25 each and pullovers for $19 each. If her total revenue from a day's production is $1492, how many of each type might she manufacture in a day? There may be multiple answers, so show the general form with k E Z and then pick different values for k to generate some possible answers.
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