Вопрос задан 18.06.2023 в 10:54. Предмет Математика. Спрашивает Мухаметзянова Алия.

Помогите Пожалуйста4. Решите систему уравнений графическим способом:{x+y=1{5x-y=5​

Смотреть ответ Спасибо) Zombynella Zombynella Ответ: В решении. Пошаговое объяснение: 4. Решите систему уравнений графическим способом: {x+y=1 {5x-y=5​ Построить графики. Графики линейной функции, прямые линии. Придать значения х, подставить в уравнение, вычислить у, записать в таблицу. Для  построения прямой достаточно двух точек, для точности построения определить три. Прежде преобразовать уравнения в уравнения функций:                    x + y = 1                                           5x - y = 5​                  у = 1 - х                                            -у = 5 - 5х                                                                           у = 5х - 5                                              Таблицы:                х  -1    0     1                                      х  -1     0     1                у   2    1     0                                     у  -10  -5     0 Согласно графиков, координаты точки их пересечения: (1; 0). Решение системы уравнений: (1; 0). 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Решение системы уравнений графическим способом

Для решения данной системы уравнений графическим способом необходимо построить графики обоих уравнений на координатной плоскости и найти точку их пересечения. Эта точка будет являться решением системы.

# Построение графиков

Для построения графиков необходимо преобразовать уравнения в уравнения функций. В данном случае, у нас есть два уравнения:

1. Уравнение 1: x + y = 1 2. Уравнение 2: 5x - y = 5

# Преобразование уравнений в уравнения функций

Для преобразования уравнений в уравнения функций, выразим переменную y через x в каждом из уравнений.

1. Уравнение 1: x + y = 1 Выразим y через x: y = 1 - x

2. Уравнение 2: 5x - y = 5 Выразим y через x: y = 5x - 5

# Построение графиков прямых

Для построения графиков прямых достаточно выбрать несколько значений для переменной x, подставить их в уравнения и вычислить соответствующие значения y. Затем эти точки можно отметить на координатной плоскости и провести прямые через них.

В данном случае, выберем значения x от -2 до 2.

| x | y в уравнении 1 | y в уравнении 2 | |-------|--------------------|--------------------| | -2 | 3 | -15 | | -1 | 2 | -10 | | 0 | 1 | -5 | | 1 | 0 | 0 | | 2 | -1 | 5 |

Теперь, отметим эти точки на координатной плоскости и проведем прямые через них.

![График системы уравнений](https://i.imgur.com/7WZtS2I.png)

# Нахождение решения системы

Точка пересечения графиков двух прямых является решением системы уравнений. В данном случае, точка пересечения имеет координаты (1, 0). Это значит, что значения x и y, равные 1 и 0 соответственно, являются решением данной системы уравнений.

# Ответ

Решение системы уравнений графическим способом: x = 1 y = 0

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