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A. Which of the following have integer solutions? Why? 1. 21x – 7y = 88 2. 55x + 44y = 99 3. 42x + 9y = 1

A. Which of the following have integer solutions? Why? 1. 21x – 7y = 88 2. 55x + 44y = 99 3. 42x + 9y = 1

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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Comprehensively solve the following. Show complete solutions. A. Which of the following have integer solutions? Why? 1. 21x - 7y = 88 2. 55x + 44y = 99 3. 42x + 9y = 1 B. Find the general solutions of the following equations. 1. 3x + 11y = 15 2. 12x + 16y = 24 3. 11x + 7y = 12 C. Solve the following. 1. A 98-pound box contains 5-pound bags of sugar and 12-pound sacks of oranges, How many of each are in the box? 2. 3x + 3y + 5z = 10 3. In a pet shop, rats cost 50 pesos, guppies cost 30 pesos and crickets cost one peso. One hundred animals are sold, and the total receipt are 1000 pesos. How many rats, guppies and crickets were sold? D. Find the remainder if 1! + 2! + 3! + + 1000! is divided by: 1. 10 2. 11 E. Solve. 1. What is the remainder if 225 is divided by 7? 2. What is the units digit of 1776177777". 3. True or False. Justify your answer. a. 17 is congruent to 5 modulo 6 b. 24 and 14 are congruent in module 6. c. -25 = 4(mod 3) 4. Complete the table for Z, under addition and multiplication.
Transcribed Image Text:Comprehensively solve the following. Show complete solutions. A. Which of the following have integer solutions? Why? 1. 21x - 7y = 88 2. 55x + 44y = 99 3. 42x + 9y = 1 B. Find the general solutions of the following equations. 1. 3x + 11y = 15 2. 12x + 16y = 24 3. 11x + 7y = 12 C. Solve the following. 1. A 98-pound box contains 5-pound bags of sugar and 12-pound sacks of oranges, How many of each are in the box? 2. 3x + 3y + 5z = 10 3. In a pet shop, rats cost 50 pesos, guppies cost 30 pesos and crickets cost one peso. One hundred animals are sold, and the total receipt are 1000 pesos. How many rats, guppies and crickets were sold? D. Find the remainder if 1! + 2! + 3! + + 1000! is divided by: 1. 10 2. 11 E. Solve. 1. What is the remainder if 225 is divided by 7? 2. What is the units digit of 1776177777". 3. True or False. Justify your answer. a. 17 is congruent to 5 modulo 6 b. 24 and 14 are congruent in module 6. c. -25 = 4(mod 3) 4. Complete the table for Z, under addition and multiplication.
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