Question

Решите графически систему уравнений с двумя переменными 2х+у=4х+у=2СРОЧНО​

Answer 1

$\underline{ \tt \huge \bigg(2; \: 0 \bigg)}$

Answer 2

To solve the system of equations graphically, we need to plot the equations on a coordinate plane and find the point of intersection, if it exists. Let's solve the system of equations 2x + y = 4 and x + y = 2.

Plotting the Equations

To plot the equations, we can rewrite them in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

For the equation 2x + y = 4: y = -2x + 4

For the equation x + y = 2: y = -x + 2

Now, we can plot these equations on a coordinate plane.

Graphical Solution

Here is the graph of the two equations:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-5, 5, 100)
y1 = -2*x + 4
y2 = -x + 2

plt.plot(x, y1, label='2x + y = 4')
plt.plot(x, y2, label='x + y = 2')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graphical Solution of the System of Equations')
plt.legend()
plt.grid(True)
plt.show()

The point of intersection of the two lines