Question

Решите систему уравнений способом подстановки: { 2(x-2y)=x-8y, 5(x+y)=2(x-y)+10; Помогите пожалуйста!!

Answer 1

2(x-2y)=x-8y,
5(x+y)=2(x-y)+10;
Преобразуем уравнения
2х - 4у = х - 8у ---> x = -4y (1)
5x + 5y = 2x - 2y + 10 ---> 7y = -3x + 10 (2)
подставим (1) в (2)
7у = -3(-4у)+ 10
7у = 12у + 10
5у = -10
у = -2 подставим в (1)
х = -4·(-2) = 8
Ответ: х = 8; у = - 2

Answer 2

Solving the System of Equations using Substitution Method

To solve the system of equations using the substitution method, we'll start by solving one of the equations for one variable and then substitute that expression into the other equation.

The given system of equations is: - 2(x-2y) = x-8y - 5(x+y) = 2(x-y)+10

Step 1: Solve the First Equation for One Variable

Let's solve the first equation for x in terms of y: - 2(x-2y) = x-8y - 2x - 4y = x - 8y - 2x - x = 4y - 8y - x = -4y

Step 2: Substitute x in the Second Equation

Now, we'll substitute the expression for x from the first equation into the second equation: - 5(x+y) = 2(x-y)+10 - 5(-4y + y) = 2(-4y - y) + 10 - 5(-3y) = 2(-5y) + 10 - -15y = -10y + 10 - -15y + 10y = 10 - -5y = 10 - y = -2

Step 3: Find the Value of x

Now that we have the value of y, we can find the value of x using the expression x = -4y: - x = -4(-2) - x = 8

Solution

So, the solution to the system of equations is: - x = 8 - y = -2

Therefore, the solution to the given system of equations using the substitution method is x = 8 and y = -2.