system of inequalities (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun Phrase

Phonetic Transcription

/sɪs.təm əv ɪn.ɪk.wɑː.lɪ.tiz/

Meaning and Usage

A system of inequalities refers to a set of two or more inequalities that have the same variables. The solutions to the system consist of all the points that satisfy all the inequalities simultaneously. It is commonly used in algebra and helps in graphing feasible regions in optimization problems, determining ranges of values, and solving real-world problems where multiple conditions coexist.

Frequency of Use

The term is frequently used in written contexts, especially in mathematics, lectures, educational materials, and examinations. While it can appear in oral discussions, it is primarily associated with formal writing such as textbooks, papers, and academic settings.

Example Sentences

1. The teacher explained how to solve a system of inequalities in her math class.

2. (Учитель объяснила, как решить систему неравенств на своем занятии по математике.)

3. In economics, a system of inequalities can represent different constraints on resources.

4. (В экономике система неравенств может представлять различные ограничения по ресурсам.)

5. The graphical solution to a system of inequalities provides a visual representation of feasible solutions.

6. (Графическое решение системы неравенств предоставляет визуальное представление приемлемых решений.)

Idiomatic Expressions

The phrase "system of inequalities" does not have a wide range of idiomatic expressions directly related to it; however, its components can contribute to several mathematical expressions:

1. "Tackle the problem head-on" - tackling a system of inequalities requires direct engagement with mathematical challenges.

2. (Решить проблему напрямую - решение системы неравенств требует непосредственного взаимодействия с математическими задачами.)

3. "Bite the bullet" - when faced with a complex system of inequalities, sometimes you just have to dive in.

4. (Сжать зубы - сталкиваясь с сложной системой неравенств, иногда просто нужно погрузиться в это.)

5. "Draw a line in the sand" - establishing clear boundaries through a system of inequalities helps define limits in practical scenarios.

6. (Нарисовать линию на песке - установка четких границ с помощью системы неравенств помогает определить ограничения в практических ситуациях.)

Etymology

The term "system" originates from the Greek word systēma, meaning "a whole composed of parts." "Inequalities" stems from the Latin inequalis, which translates to "unequal." Thus, "system of inequalities" combines the notions of interconnected parts and comparative values.

Synonyms and Antonyms

Synonyms

• Set of inequalities
• Group of inequalities
• System of equations (when talking about similar structures)

Antonyms

• System of equalities
• Single inequality
• Independent equations

This comprehensive breakup provides a solid foundation for understanding "system of inequalities" in mathematical contexts.