Question

Решите систему линейных уравнений методом сложения. 1){3x-7y=11{6x+7y=16 2){4x+2y=5 {4x-6y=-7 3){2x-3y=8 {7x-5y=-5. Заранее спасибо Смотреть ответ vydra52 vydra52 1){3х-7у=11|×(-2) {6х+7у=16 + {-6х+14у=-22 {6х+7у=16 6х-6х+7у+14у=-22+16 21 у=-6 у=-3\11(дробь) 2){4х+2у=5 {4х-6у=-7|÷(-1) +{4х+2у=5 {-4х+6у=7 4х-4х+6у+2у=5+7 8у=12 у=1,5 3){2х-3у=8|×5 {7х-5у=-5|×(-3) +{10х-15у=40 {-21х+15у=15 10х-21х+15у-15у=40-15 -11х=25 х=-2 5/11(минус две целых,пять одиннадцатых) Новые вопросы в Алгебра ПОМОГИТЕ ПОЖАЛУЙСТА!!! алгебра 7 класс! фото прикреплю, задание не очень сложное, но я не могу решит) Шахматист играет не менее одной партии в день и не более 12 за любую неделю (неде-ля начинается в понедельник и заканчивается в воскресенье). Докажите … , что найдется несколько подряд идущих дней, за которые он сыграет ровно 20 партий. морская вода содержит 5% солей.Сколько чистой воды надо добавить в 40 литров морской воды,чтобы процент соли был 2%​ найдите числа M и N, чтобы выполнялось равенство (фото ниже) если не тяжело, то с подробным решением Найдите такие числа M и N, чтобы выполнялось равенство(фото ниже) если не тяжело, то с подробным решением ^@[email protected]^ 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

Для решения системы линейных уравнений методом сложения, следует следующий шаги:

1. Решение системы уравнений 1: {3x - 7y = 11 {6x + 7y = 16

Сложим оба уравнения, чтобы избавиться от y: (3x - 7y) + (6x + 7y) = 11 + 16 9x = 27 x = 27 / 9 x = 3

Теперь подставим x в одно из уравнений для нахождения y: 3x - 7y = 11 3 * 3 - 7y = 11 9 - 7y = 11 -7y = 11 - 9 -7y = 2 y = 2 / (-7) y = -2/7 (или -0.2857)

Таким образом, решение первой системы: x = 3, y = -2/7.

2. Решение системы уравнений 2: {4x + 2y = 5 {4x - 6y = -7

Для удобства, домножим первое уравнение на 3, а второе на 1: 3 * (4x + 2y) = 3 * 5 4x - 6y = -7

Теперь сложим оба уравнения: (4x + 2y) + (4x - 6y) = 5 + (-7) 8x - 4y = -2

Теперь, чтобы избавиться от x, домножим первое уравнение на -1 и сложим с полученным предыдущим уравнением: -1 * (4x + 2y) + (8x - 4y) = -1 * 5 + (-2) -4x - 2y + 8x - 4y = -5 - 2 4x - 6y = -7

Мы получили ту же систему уравнений, что и в начале. Это означает, что система имеет бесконечно много решений. В данном случае, можно сократить одно из уравнений:

4x - 6y = -7 (4x - 6y) / 2 = -7 / 2 2x - 3y = -7/2

Теперь, используем полученное уравнение и систему 3 для нахождения значения x:

3. Решение системы уравнений 3: {2x - 3y = 8 {7x - 5y = -5

Умножим первое уравнение на 5 и второе на 3: 5 * (2x - 3y) = 5 * 8 7 * (7x - 5y) = 7 * (-5)

10x - 15y = 40 49x - 35y = -35

Теперь сложим оба уравнения: (10x - 15y) + (49x - 35y) = 40 - 35 59x - 50y = 5

Теперь решим полученное уравнение относительно x: 59x = 5 + 50y x = (5 + 50y) / 59

Таким образом, мы нашли x в виде функции от y.

Сводная таблица решений:

1. x = 3, y = -2/7
2. Бесконечно много решений вида 2x - 3y = -7/2
3. x = (5 + 50y) / 59

Пожалуйста, убедитесь, что решение системы 2 имеет одну и ту же систему уравнений, и, возможно, есть ошибка в изначальной системе, что привело к такому результату. Если у вас возникнут дополнительные вопросы, не стесняйтесь задать их.