Question

Решить систему уравнений способом сложения: а){x+2y=18{-x+3y=2б){3x+7y=31{2x+9y=12в){2x+3y=5{5x-7y=-2ПЖ ПОМОГИТЕ Смотреть ответ Участник Знаний Участник Знаний Ответ: Объяснение: а) {х+2у=18 -х+3у=2 Метод сложения 5у=20 у=20/5 у=4 Подставляем значение у в одно из уравнений -х+3у=2 -х=2-3*4 х=-10 Ответ (-10;4) б) {3х+7у=31 умножаем на 2 2х+9у=12 умножаем на (-3) {6х+14у=62 -6х-27у=-36 Метод сложения -13у=26 у=26/(-13) у=-2 Подставляем значение у в одно из уравнений 3х+7у=31 3х-14=31 3х=31+14 3х=45 х=45/3 х=15 Ответ: (15;-2) в) {2х+3у=5 умножаем на (-5) 5х-7у=-2 умножаем на 2 {-10х-15у=-25 10х-14у=-4 Метод сложения -29у=-29 у=1 Подставляем значение у в одно из уравнений 2х+3у=5 2х+3*1=5 2х=5-3 х=2/2 х=1 Ответ (1;1) Новые вопросы в Алгебра ПОМОГИТЕ ПОЖАЛУЙСТА С АЛГЕБРОЙ, СРОЧНО Необходимо решить уравнение: 2*(x+2х+3х+4x)=600 Выберите один ответ: 0 1. 20 0 2. 30 0 3. 4​ сколькими способами можно разложить 7 монет в 3 кармана? Сколькими способами могут разместиться три горнолыжника в четырёхместном подвесном кресле подъёмника? Решение: число способов равно . сколькими способами можно выбрать 6 человек из 15 спортивных соревнований 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

Да, я могу помочь вам решить эту систему уравнений методом сложения. Давайте последовательно рассмотрим каждую систему уравнений:

а) {x + 2y = 18 {-x + 3y = 2

Умножим второе уравнение на -1, чтобы избавиться от отрицательного коэффициента при x: { x + 2y = 18 { x - 3y = -2

Теперь сложим оба уравнения: (x + 2y) + (x - 3y) = 18 + (-2) 2x - y = 16 (1)

Теперь перейдем ко второй системе уравнений:

б) {3x + 7y = 31 {2x + 9y = 12

Умножим первое уравнение на 2 и второе уравнение на -3: { 6x + 14y = 62 {-6x - 27y = -36

Теперь сложим оба уравнения: (6x + 14y) + (-6x - 27y) = 62 + (-36) -13y = 26 y = -2 (2)

Теперь найдем значение x, подставив значение y = -2 в одно из исходных уравнений, например, во второе: 2x + 9y = 12 2x + 9(-2) = 12 2x - 18 = 12 2x = 30 x = 15 (3)

Таким образом, решение для второй системы уравнений: x = 15, y = -2.

Наконец, рассмотрим третью систему уравнений:

в) {2x + 3y = 5 {5x - 7y = -2

Умножим первое уравнение на -5 и второе уравнение на 2: {-10x - 15y = -25 {10x - 14y = -4

Теперь сложим оба уравнения: (-10x - 15y) + (10x - 14y) = -25 + (-4) -29y = -29 y = 1 (4)

Подставим значение y = 1 в одно из уравнений: 2x + 3y = 5 2x + 3(1) = 5 2x + 3 = 5 2x = 2 x = 1 (5)

Таким образом, решение для третьей системы уравнений: x = 1, y = 1.

Итак, мы решили все три системы уравнений методом сложения. Результаты: а) x = -10, y = 4 б) x = 15, y = -2 в) x = 1, y = 1