Question

2. Решите системы уравнений способом подстановки x+2y 3x-4y=1.​

Answer 1

Решение системы уравнений способом подстановки:

1. Решим первое уравнение относительно x:

x + 2y = 1 - 3x + 4y

4x = 1 - 2y - 4y

4x = 1 - 6y

x = (1 - 6y) / 4

2. Подставим выражение для x во второе уравнение:

3x - 4y = 1

3((1 - 6y) / 4) - 4y = 1

(3 - 18y) / 4 - 4y = 1

3 - 18y - 16y = 4

-34y = 1

y = -1/34

3. Найдем x, подставив значение y в первое уравнение:

x + 2y = 1

x + 2(-1/34) = 1

x = 1 + 2/34

x = 37/34

Ответ: x = 37/34, y = -1/34.

Answer 2

Solving the System of Equations using the Substitution Method

To solve the system of equations x + 2y = 3 and 3x - 4y = 1 using the substitution method, we will solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for x: x = 3 - 2y.

Now, substitute this value of x into the second equation: 3(3 - 2y) - 4y = 1.

Simplifying the equation: 9 - 6y - 4y = 1, 9 - 10y = 1, -10y = -8, y = 0.8.

Now, substitute the value of y back into the first equation to find x: x = 3 - 2(0.8), x = 3 - 1.6, x = 1.4.

Therefore, the solution to the system of equations is x = 1.4 and y = 0.8.