be chosen to satisfy The last two of the must have a positiv values Chang obtain PROBLEMS 2.5 1. Which of the follov (a) 6x +51y = 22 (b) 33x + 14y (c) 14x +35y = 9 2. Determine all solut (a) 56x +72y = 4 (b) 24x + 138y = (c) 221x +35y = 3. Determine all soluti (a) 18x +5y = 48 (b) 54x +21y = 9 (c) 123x + 360y = (d) 158x - 57y = %3D %3D %3D %3D
be chosen to satisfy The last two of the must have a positiv values Chang obtain PROBLEMS 2.5 1. Which of the follov (a) 6x +51y = 22 (b) 33x + 14y (c) 14x +35y = 9 2. Determine all solut (a) 56x +72y = 4 (b) 24x + 138y = (c) 221x +35y = 3. Determine all soluti (a) 18x +5y = 48 (b) 54x +21y = 9 (c) 123x + 360y = (d) 158x - 57y = %3D %3D %3D %3D
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 58PPS
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
1a,b,c
Transcribed Image Text:A little further effort produces all solutions in the positive integers. For this, t must
be chosen to satisfy simultaneously the inequalities
4t > 0
25 – 7t > 0
75 + 3t > 0
The last two of these are equivalent to the requirement -25 < t < 3÷. Because t
must have a positive value, we conclude that t = 1, 2, 3, leading to precisely the
values Chang obtained.
%3D
PROBLEMS 2.5
1. Which of the following Diophantine equations cannot be solved?
(a) 6x +51y = 22.
(b) 33x + 14y = 115.
(c) 14x + 35y = 93.
2. Determine all solutions in the integers of the following Diophantine equations:
(a) 56x +72y = 40.
(b) 24x + 138y = 18.
(c) 221x +35y = 11.
3. Determine all solutions in the positive integers of the following Diophantine equations:
(a) 18x +5y = 48.
(b) 54x +21y = 906.
(c) 123x +360y = 99.
(d) 158x -57y =7.
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