Question

Ребята,срочно нужна помощь! Решите систему уравнений: {5p-3q=0, {3p+4q=29; Нужно сделать двумя способами: 1)графическим 2)системным Прошу помогите,дам 30 баллов!!

Answer 1

15p-9q=0
 15p+20q=29 -29q=-29 15p-9q=0 q=1 15p=9 q=1 p=0,6

Answer 2

System of Equations: Graphical and Systematic Solutions

To solve the given system of equations, we will use two methods: graphical and systematic. Let's begin!

Graphical Solution:

To solve the system of equations graphically, we will plot the equations on a coordinate plane and find the point of intersection, which represents the solution.

The given system of equations is: Equation 1: 5p - 3q = 0 Equation 2: 3p + 4q = 29

To graph Equation 1, we can rearrange it to solve for q: 5p - 3q = 0 -3q = -5p q = (5/3)p

To graph Equation 2, we can rearrange it to solve for q: 3p + 4q = 29 4q = -3p + 29 q = (-3/4)p + 29/4

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

import matplotlib.pyplot as plt
import numpy as np

p = np.linspace(-10, 10, 100)
q1 = (5/3) * p
q2 = (-3/4) * p + 29/4

plt.plot(p, q1, label='5p - 3q = 0')
plt.plot(p, q2, label='3p + 4q = 29')
plt.xlabel('p')
plt.ylabel('q')
plt.title('Graphical Solution')
plt.legend()
plt.grid(True)
plt.show()

The point of intersection of the two lines represents the solution to the system of equations. By analyzing the graph, we can estimate the approximate values of p and q.

Systematic Solution:

To solve the system of equations systematically, we will use the method of substitution or elimination. Let's use the method of substitution:

Step 1: Solve Equation 1 for p: 5p - 3q = 0 5p = 3q p = (3/5)q

Step 2: Substitute the value of p in Equation 2: 3p + 4q = 29 3((3/5)q) + 4q = 29 (9/5)q + 4q = 29 (9q + 20q) / 5 = 29 29q / 5 = 29 29q = 29 * 5 29q = 145 q = 145 / 29 q = 5

Step 3: Substitute the value of q in Equation 1 to find p: 5p - 3q = 0 5p - 3(5) = 0 5p - 15 = 0 5p = 15 p = 15 / 5 p = 3

Therefore, the solution to the given system of equations is p = 3 and q = 5.

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