Question

4x-5y=1 2x-3y=2 Алгебра 7 класс метод подстановки

Answer 1

Выразим х из второго уравнения:

2х=3у+2

х=1,5у+1

и подставим его в первое уравнение:

4(1,5у+1)-5у=1

Решаем полученное уравнение с одним неизвестным (находим у):

6у+4-5у=1

у=1-4

у=-3

Находим х:

х=1,5*(-3)+1=-4,5+1=-3,5

Ответ. (-3,5;  -3) 

Answer 2

Problem Statement

We are given the following system of equations: - Equation 1: 4x - 5y = 1 - Equation 2: 2x - 3y = 2

We are asked to solve this system of equations using the method of substitution.

Solution

To solve the system of equations using the method of substitution, we will solve one equation for one variable and substitute it into the other equation.

Let's solve Equation 1 for x: 4x - 5y = 1

Solving for x, we get: 4x = 1 + 5y x = (1 + 5y) / 4

Now, substitute this value of x into Equation 2: 2x - 3y = 2

Substituting x = (1 + 5y) / 4, we get: 2((1 + 5y) / 4) - 3y = 2

Simplifying the equation, we have: (2 + 10y) / 4 - 3y = 2

Multiplying both sides of the equation by 4 to eliminate the fraction, we get: 2 + 10y - 12y = 8

Combining like terms, we have: -2y = 6

Dividing both sides of the equation by -2, we get: y = -3

Now, substitute this value of y back into Equation 1 to find x: 4x - 5(-3) = 1 4x + 15 = 1 4x = 1 - 15 4x = -14 x = -14 / 4 x = -7/2

Therefore, the solution to the system of equations is: x = -7/2 and y = -3.

Note: The solution to the system of equations is x = -7/2 and y = -3.