Question

Докажите что система уравнений имеет бесконечное число решений 1){7х+8у=11 {14х+16у=22 Смотреть ответ stalbekovbayel009 stalbekovbayel009 Ответ: Система уравнений имеет бесконечное число решений (множество решений выражается через параметры), если одно уравнение можно выразить через другое с помощью алгебраических операций. Рассмотрим данную систему уравнений: {7x + 8y = 11 {14x + 16y = 22 Первое уравнение можно переписать как: 7x = 11 - 8y Тогда второе уравнение можно переписать, подставив вместо 7x: 14(11 - 8y)/7 + 16y = 22 Упрощаем: 22 - 16y + 16y = 22 Таким образом, мы получили тождественное уравнение 22 = 22, которое верно при любых значениях y. Теперь рассмотрим любое значение y (например, y = 0). Подставим его в выражение для 7x = 11 - 8y: 7x = 11 - 8*0 = 11 Тогда x = 11/7. Мы получили решение системы уравнений при конкретном значении y = 0 и любом другом значении y. Создано бесконечное число решений системы уравнений. Бомба ЛУЧШИЙ Новые вопросы в Математика 5. Три звонка звенят каждые 18, 24 и 30 минут соответственно. Они зазвонили вместе в 11:00. Во сколько часов они зазвонят вместе еще раз? Д 15:30 B) 1 … 6:00 C) 16:20 D) 17:00​ 7.8×-4.6×+0.85=12 рівняння якщо що Знайди середнє арифметичне -5,8 i 2,6 СРОЧНО ДАЮ 15 ОЧКОВ помогите! |х – 3| = –3 1) 3 2) 0 3)–3 1,2 – (х + 1,6) 1)-0 … ,4 – х 2)-0,4 + х 3)0,4 – х 4)0,4 + х Предыдущий Следующий Вместе мы знаем больше Этот сайт использует cookies Политика Cookies . Вы можете указать условия хранения и доступ к cookies в своем браузере. 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Answer 1

Верно, данная система уравнений имеет бесконечное число решений. Как вы правильно указали, первое уравнение можно выразить через второе с помощью алгебраических операций. Перепишем первое уравнение:

7x + 8y = 11

Выразим x через y:

7x = 11 - 8y x = (11 - 8y)/7

Теперь подставим полученное значение x во второе уравнение:

14x + 16y = 22

Подставляем выражение для x:

14((11 - 8y)/7) + 16y = 22

Упрощаем:

22 - 16y + 16y = 22

Получаем тождественное уравнение 22 = 22, которое верно при любых значениях y.

Таким образом, любое значение y является решением системы уравнений. Например, при y = 0 получаем:

x = (11 - 8*0)/7 = 11/7

Таким образом, при любом значении y (включая y = 0) получается соответствующее значение x. Так как y может принимать любое число, система имеет бесконечное число решений, выражаемых через параметры.