Question

1) {2x+y=4 {y=2x 2) {x+y=6 {2x+2y=12 3) {2x+y=4 {5x-2y=1 По третьему примеру составите таблицу и график по помогите

Answer 1

РЕШАЕМ системы уравнений.
1) Метод подстановки - ур.2) подставим в ур. 1)
2х + 2х = 4
4х = 4
х = 1 - ответ
у = 2х = 2 - ответ
2) Уравнения одинаковые -
ОТВЕТ - множество решений (при любых Х и У)
3) Решаем графически.  
Преобразуем параметрические уравнения к каноническому уравнению прямой - Y = k*X + b.
первая прямая  = Y = - 2x+ 4
вторая прямая = Y = 2.5*X - 0.5
Делаем чертеж.
Х= 1 и У = 2 - ОТВЕТ

Answer 2

Problem Statement

We have the following system of equations: 1) 2x + y = 4 2) y = 2x + 2 3) x + y = 6 4) 2x + 2y = 12

We need to create a table and a graph based on the third example.

Solution

To solve this system of equations, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the substitution method.

From equation 2, we have y = 2x + 2. We can substitute this value of y into equations 1 and 3 to eliminate y.

Substituting y = 2x + 2 into equation 1, we get: 2x + (2x + 2) = 4 Simplifying, we have: 4x + 2 = 4 4x = 2 x = 1/2

Substituting y = 2x + 2 into equation 3, we get: x + (2x + 2) = 6 Simplifying, we have: 3x + 2 = 6 3x = 4 x = 4/3

So, we have found the values of x. Now, we can substitute these values back into equation 2 to find the corresponding values of y.

Substituting x = 1/2 into equation 2, we get: y = 2(1/2) + 2 y = 1 + 2 y = 3

Substituting x = 4/3 into equation 2, we get: y = 2(4/3) + 2 y = 8/3 + 2 y = 14/3

Therefore, the solution to the system of equations is: x = 1/2, y = 3 and x = 4/3, y = 14/3.

Table

We can create a table to represent the values of x and y for each equation in the system:

| Equation | x | y | |----------|---|---| | 1) 2x + y = 4 | 1/2 | 3 | | 2) y = 2x + 2 | 1/2 | 3 | | 3) x + y = 6 | 1/2 | 3 | | 4) 2x + 2y = 12 | 1/2 | 3 |

Graph

We can also plot the graph of the system of equations on a coordinate plane. Let's plot the equations:

Equation 1: 2x + y = 4 Simplifying for y, we get: y = -2x + 4

Equation 2: y = 2x + 2

Equation 3: x + y = 6 Simplifying for y, we get: y = -x + 6

Equation 4: 2x + 2y = 12 Simplifying for y, we get: y = -x + 6

Now, let's plot these equations on a graph:


The intersection points of the lines represent the solutions to the system of equations. In this case, we have two intersection points: (1/2, 3) and (4/3, 14/3).

I hope this helps! Let me know if you have any further questions.