Question

Решите систему уравнений 2x - 3(2y + 1) = 15 3(x + 1 ) + 3y = 2y - 2 Способом сложения

Answer 1

Способ сложения решения систем уравнений .

$\left\{\begin{array}{l}2x-3(2y+1)=15\\3(x+1)+3y=2y-2\end{array}\right\ \ \left\{\begin{array}{l}2x-6y-3=15\\3x+3+3y=2y-2\end{array}\right\ \ \left\{\begin{array}{l}2x-6y=18\ |:2\\3x+y=-5\end{array}\right$

$\left\{\begin{array}{l}x-3y=9\\3x+y=-5\ |\cdot 3\end{array}\right\ \oplus\ \left\{\begin{array}{l}3y=x-9\\10x=-6\end{array}\right\ \ \left\{\begin{array}{l}3y=-9,6\\x=-0,6\end{array}\right\ \ \left\{\begin{array}{l}y=-3,2\\x=-0,6\end{array}\right$

Ответ:  ( -0,6 : -3,2 ) .

Answer 2

Problem Statement

We are given the following system of equations:

Equation 1: 2x - 3(2y + 1) = 15

Equation 2: 3(x + 1) + 3y = 2y - 2

We need to solve this system of equations using the method of addition.

Solution

To solve the system of equations using the method of addition, we will eliminate one variable by adding the two equations together. Let's start by simplifying the equations.

Equation 1: 2x - 3(2y + 1) = 15

Simplifying Equation 1: 2x - 6y - 3 = 15 2x - 6y = 18

Equation 2: 3(x + 1) + 3y = 2y - 2

Simplifying Equation 2: 3x + 3 + 3y = 2y - 2 3x + 3y = 2y - 5

Now, we can add the two equations together to eliminate the variable 'y'.

(2x - 6y) + (3x + 3y) = 18 + (2y - 5)

Simplifying the equation: 5x - 3y = 2y + 13

Now, we have a new equation: 5x - 3y = 2y + 13.

To solve for 'x', we need to isolate the variable 'x' on one side of the equation. Let's move the '2y' term to the left side.

5x - 3y - 2y = 13

Simplifying the equation: 5x - 5y = 13

Now, we have a new equation: 5x - 5y = 13.

To solve for 'x', we can divide both sides of the equation by 5.

(5x - 5y) / 5 = 13 / 5

Simplifying the equation: x - y = 13/5

Now, we have a new equation: x - y = 13/5.

To solve for 'y', we can substitute the value of 'x' from this equation into either Equation 1 or Equation 2. Let's substitute it into Equation 1.

2x - 6y = 18

Substituting x - y = 13/5 into Equation 1: 2(13/5) - 6y = 18

Simplifying the equation: 26/5 - 6y = 18

To solve for 'y', we need to isolate the variable 'y' on one side of the equation. Let's move the constant term to the right side.

26/5 - 6y = 18 -6y = 18 - 26/5

Simplifying the equation: -6y = (90 - 26)/5 -6y = 64/5

Now, we have a new equation: -6y = 64/5.

To solve for 'y', we can divide both sides of the equation by -6.

(-6y) / -6 = (64/5) / -6

Simplifying the equation: y = -64/30

Now, we have found the value of 'y': y = -64/30.

To find the value of 'x', we can substitute the value of 'y' into Equation 1.

2x - 3(2y + 1) = 15

Substituting y = -64/30 into Equation 1: 2x - 3(2(-64/30) + 1) = 15

Simplifying the equation: 2x - 3(-128/30 + 1) = 15 2x - 3(-128/30 + 30/30) = 15 2x - 3(-128/30 + 30/30) = 15 2x - 3(-98/30) = 15 2x + 294/30 = 15

To solve for 'x', we need to isolate the variable 'x' on one side of the equation. Let's move the constant term to the right side.

2x + 294/30 = 15 2x = 15 - 294/30

Simplifying the equation: 2x = (450 - 294)/30 2x = 156/30

Now, we have a new equation: 2x = 156/30.

To solve for 'x', we can divide both sides of the equation by 2.

(2x) / 2 = (156/30) / 2

Simplifying the equation: x = 156/60

Now, we have found the value of 'x': x = 156/60.

Therefore, the solution to the system of equations is: x = 156/60 y = -64/30

Note: The values of 'x' and 'y' are in fractional form. They can be simplified further if needed.

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