Question

(2x + 1)²-(2x - y) (2x + y) = (y + 8) (y-10), 4x (x-5)-(2x-3) (2x-9)=6y-104;​

Answer 1

Ответ:

Сначала упростим уравнения, раскрыв скобки и приведя подобные члены . Затем решим систему методом сложения (из 1 уравнения вычтем 2 уравнение) .

$\left\{\begin{array}{l}(2x+1)^2-(2x-y)(2x+y)=(y+8)(y-10)\\4x(x-5)-(2x-3)(2x-9)=6y-104\end{array}\right\\\\\\\left\{\begin{array}{l}4x^2+4x+1-(4x^2-y^2)=y^2-2y-80\\4x^2-20x-(4x^2-24x+27)=6y-104\end{array}\right\ \ \left\{\begin{array}{l}4x+1=-2y-80\\4x-27=6y-104\end{array}\right$

$\left\{\begin{array}{l}4x+2y=-81\\4x-6y=-77\end{array}\right\ \ominus \ \left\{\begin{array}{l}4x+2y=-81\\8y=-4\end{array}\right\ \ \left\{\begin{array}{l}4x=-2y-81\\y=-\dfrac{1}{2}\end{array}\right$  

$\left\{\begin{array}{l}4x=1-81\\\ y=-\dfrac{1}{2}\end{array}\right\ \ \left\{\begin{array}{l}4x=-80\\y=-\dfrac{1}{2}\end{array}\right\ \ \left\{\begin{array}{l}\bf x=-20\\\bf y=-0,5\end{array}\right\\\\\\\boldsymbol{Otvet:\ \ (-20\, ;-0,5\ )\ .}$    

Answer 2

Ответ:

Объяснение:

(2x + 1)²-(2x - y) (2x + y) = (y + 8) (y-10)

4х²+4х+1-4х²+у²=у²-2у-80

4х+1=-2у-80

4х+2у=-81

4x (x-5)-(2x-3) (2x-9)=6y-104

4х²-20х-4х²+24х-27=6у-104

4х-27=6у-104

4х-6у=-77

4х+2у=-81

4х-6у=-77

-81-2у=-77+6у;   -8у=-4;  у=0,5

4х+0,5*2=-81;  4х+1=-81;  4х=-82;  х=-20,5

Ответ: (-20,5;  0,5)

Answer 3

Let's solve the given system of equations step by step.

Equation 1: (2x + 1)² - (2x - y)(2x + y) = (y + 8)(y - 10)

Expanding the square and simplifying, we get: (4x² + 4x + 1) - (4x² - y²) = (y² - 2y - 80)

Simplifying further, we have: 4x + 1 + y² = y² - 2y - 80

Rearranging the terms, we get: 4x + 1 + 2y = -2y - 80

Combining like terms, we have: 4x + 2y + 2y = -80 - 1

Simplifying, we get: 4x + 4y = -81 ...........(Equation A)

Equation 2: 4x(x - 5) - (2x - 3)(2x - 9) = 6y - 104

Expanding and simplifying, we have: 4x² - 20x - (4x² - 18x - 6x + 27) = 6y - 104

Simplifying further, we get: 4x² - 20x - 4x² + 18x + 6x - 27 = 6y - 104

Combining like terms, we have: -2x - 27 = 6y - 104

Rearranging the terms, we get: -2x - 6y = -104 + 27

Simplifying, we have: -2x - 6y = -77 ...........(Equation B)

Now, we have a system of equations:

Equation A: 4x + 4y = -81 Equation B: -2x - 6y = -77

We can solve this system by using any method, such as substitution or elimination. Let's use the elimination method.

Multiplying Equation A by 3 and Equation B by 2, we get:

Equation A (multiplied by 3): 12x + 12y = -243 Equation B (multiplied by 2): -4x - 12y = -154

Adding these two equations together, we eliminate the variable "y":

(12x + 12y) + (-4x - 12y) = -243 + (-154)

Simplifying, we have: 12x - 4x = -243 - 154

Combining like terms, we get: 8x = -397

Dividing both sides by 8, we find: x = -397/8

Substituting the value of x into Equation A, we can solve for y:

4x + 4y = -81

Substituting x = -397/8, we have: 4(-397/8) + 4y = -81

Simplifying, we get: -397 + 32y = -648

Rearranging the terms, we have: 32y = -648 + 397

Simplifying further, we get: 32y = -251

Dividing both sides by 32, we find: y = -251/32

Therefore, the solution to the given system of equations is: x = -397/8 y = -251/32