Question

(x-2)(y-10)=(x+1)(y-4) (2x-1)(5y+4)=2(5x-1)(y-1)-14 Решите эту систему уравнений с двумя переменными с 2 неизвестными методом замены

Answer 1

Ответ:

{(x-2)(y-10)=(x+1)(y-4)

{(2x-1)(5y+4)=2(5x-1)(y-1)-14

{xy-10x-2y+20=xy-4x+y-4

{10xy+8x-5y-4=10xy-10x-2y+4-14

{-6x-3y=-24

{18x-3y=-6 |•(-1)

{-6x-3y=-24

{-18x+3y=6

Прибавляем системы

-24x=-18

x=3/4

Вместо х поставим 3/4

-6•3/4-3y=-24

-4,5-3y=-24

-3y=-19,5

y=6,5

Ответ: x=3/4 ; y=6,5

Answer 2

Solving the System of Equations

To solve the system of equations:

(x-2)(y-10) = (x+1)(y-4) (2x-1)(5y+4) = 2(5x-1)(y-1) - 14

We will use the method of substitution.

Let's solve the first equation for x:

(x-2)(y-10) = (x+1)(y-4)

Expanding both sides of the equation, we get:

xy - 10x - 2y + 20 = xy + x - 4y - 4

Simplifying the equation, we have:

-10x - 2y + 20 = x - 4y - 4

Rearranging the terms, we get:

-11x + 2y = -24 ----(1)

Now, let's solve the second equation for x:

(2x-1)(5y+4) = 2(5x-1)(y-1) - 14

Expanding both sides of the equation, we get:

10xy + 8x - 5y - 4 = 10xy - 2y - 10x - 2

Simplifying the equation, we have:

8x - 5y - 4 = -2y - 10x - 2

Rearranging the terms, we get:

18x - 3y = -2 ----(2)

Now we have a system of two equations:

-11x + 2y = -24 ----(1) 18x - 3y = -2 ----(2)

To solve this system, we can use the method of substitution. We can solve equation (1) for x and substitute it into equation (2).

From equation (1), we can solve for x:

-11x + 2y = -24

Rearranging the terms, we get:

-11x = -2y - 24

Dividing both sides by -11, we get:

x = (2y + 24) / 11

Now, substitute this value of x into equation (2):

18x - 3y = -2

Substituting the value of x, we get:

18((2y + 24) / 11) - 3y = -2

Simplifying the equation, we have:

36y + 432 - 33y = -22

Combining like terms, we get:

3y + 432 = -22

Subtracting 432 from both sides, we get:

3y = -454

Dividing both sides by 3, we get:

y = -454 / 3

Now, substitute this value of y back into equation (1) to find x:

-11x + 2y = -24

Substituting the value of y, we get:

-11x + 2(-454 / 3) = -24

Simplifying the equation, we have:

-11x - 908 / 3 = -24

Adding 908 / 3 to both sides, we get:

-11x = -24 + 908 / 3

Combining like terms, we get:

-11x = -72 / 3

Simplifying the right side, we have:

-11x = -24 + 302.67

-11x = 278.67

Dividing both sides by -11, we get:

x = -278.67 / 11

Therefore, the solution to the system of equations is:

x = -25.33 y = -151.33

Please note that the solution is approximate due to the decimal values involved.

Let me know if you need any further assistance!