Question

Решение системы линейных уравнений с двумя переменными способом подстановки (3Y+X=5 ( 13y-2x=11

Answer 1

Из первого уравнения находим х
x=5-3y
Подставляем полученное значение во второе уравнение
13y-2(5-3y)=11
13y-10+6y=11
19y=21
y=21/19
$y=1 \frac{2}{19}$
Теперь находим х
$x=5-3* \frac{21}{19} =5- \frac{63}{19} =5-3 \frac{6}{19} = \frac{13}{19}$
Ответ: (13/19; 21/19)

Answer 2

Solving a System of Linear Equations with Two Variables using Substitution Method

To solve the system of linear equations with two variables using the substitution method, we'll start with the given equations: 1. 3y + x = 5 2. 13y - 2x = 11

Step 1: Solve for one variable in terms of the other

We can solve the first equation for x in terms of y: x = 5 - 3y

Step 2: Substitute the expression for one variable into the other equation

Now, we substitute the expression for x into the second equation: 13y - 2(5 - 3y) = 11

Step 3: Solve for the remaining variable

We solve for y: 13y - 10 + 6y = 11 19y - 10 = 11 19y = 21 y = 21 / 19 y = 1.1053

Step 4: Substitute the value of y back into one of the original equations to solve for the other variable

Using the first equation: 3(1.1053) + x = 5 x = 5 - 3.3159 x = 1.6847

Solution:

The solution to the system of linear equations is: x ≈ 1.6847 y ≈ 1.1053