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 Diophanti (a) 56x + 72y = 40. (b) 24x + 138y = 18. (c) 221x +35y = 11. %3D %3D %3D %3D %3D
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![III tme positive integers. For this, t must
DU UIIUJCII IU salisry simultaneously the inequalities
4t > 0
25 – 7t > 0
75 + 3t > 0
The last two of these are equivalent to the requirement -25 < t < 3ª. Because t
must have a positive value, we conclude that t = 1, 2, 3, leading to precisely the
values Chang obtained.
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 +35 y = 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bf7da54-5138-4b57-a0f9-aec30fa8e8cf%2F4071ee25-8bbe-4a58-bc79-8ad17ad1a733%2Fr5djpdl_processed.jpeg&w=3840&q=75)
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