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Розвяжіть систему рівнянь {х+у=2 {2х²-ху=65 З поясненням Смотреть ответ SergeySergeev1589 SergeySergeev1589 {x+y=2; {2x²-xy=65; {y=2-x; x(2x-2+x)=65; x(3x-2)=65 3x²-2x-65=0 D=4+780=784;√D=28 x₁,₂=(2±28)/6=5;-13/3 y=-3;19/3 Новые вопросы в Алгебра 5-2(х-1)=4-х Помогите решыть ! 3(x-2)=x+2 помогите решыть розвʼяжіть систему рівнянь х-у=5 х+у=1 А.(-2;3) Б.(6;1) В.(-2;3) Г.(3;-2) Басейн наповнюється двома трубами за 4 години. За скільки годин наповнить цей басейн кожна труба окремо, коли відомо, що продуктивність однієї з них у … 2,5 рази вища від продуктивності другої? Допоможіть будь ласка y = x ^ 2 - 8|x| + 7 зробіть графік​ Предыдущий Следующий Вместе мы знаем больше Этот сайт использует cookies Политика Cookies . Вы можете указать условия хранения и доступ к cookies в своем браузере. 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Answer 1

To solve the system of equations {x + y = 2, 2x² - xy = 65}, we can use the method of substitution or elimination. I'll demonstrate the elimination method here.

Step 1: Solve the first equation for y in terms of x: x + y = 2 y = 2 - x

Step 2: Substitute the expression for y from Step 1 into the second equation: 2x² - xy = 65 2x² - x(2 - x) = 65 2x² - 2x + x² = 65 3x² - 2x - 65 = 0

Step 3: Solve the quadratic equation 3x² - 2x - 65 = 0. We can use the quadratic formula for this:

The quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

In our case, a = 3, b = -2, and c = -65:

x = (2 ± √((-2)² - 4 * 3 * (-65))) / 2 * 3 x = (2 ± √(4 + 780)) / 6 x = (2 ± √784) / 6 x = (2 ± 28) / 6

Now, we have two potential solutions for x:

1. x₁ = (2 + 28) / 6 = 30 / 6 = 5
2. x₂ = (2 - 28) / 6 = -26 / 6 = -13/3

Step 4: Find the corresponding values of y using the expression y = 2 - x:

For x₁ = 5: y = 2 - 5 = -3

For x₂ = -13/3: y = 2 - (-13/3) = 2 + 13/3 = 19/3

So, the solutions to the system are (x₁, y₁) = (5, -3) and (x₂, y₂) = (-13/3, 19/3).

Now, for the other questions you asked:

1. 5 - 2(x - 1) = 4 - x: To solve this equation, first distribute the -2 on the left side: 5 - 2x + 2 = 4 - x Then, combine like terms: -2x + 7 = 4 - x Now, move the x term to one side: -2x + x = 4 - 7 -x = -3 Finally, divide by -1 to find x: x = 3

2. 3(x - 2) = x + 2: Distribute the 3 on the left side: 3x - 6 = x + 2 Move the x term to one side: 3x - x = 2 + 6 2x = 8 Divide by 2 to find x: x = 4

3. The system of equations x - y = 5 and x + y = 1 can be solved using the elimination method:

Add the two equations to eliminate y: (x - y) + (x + y) = 5 + 1 2x = 6 Divide by 2 to find x: x = 3

Now, substitute the value of x into one of the original equations to find y: x + y = 1 3 + y = 1 y = 1 - 3 y = -2

So, the solution to the system is (x, y) = (3, -2).

4. To determine how long it takes each pipe to fill the pool individually, we need more information about the pool's total capacity and the combined rate at which both pipes fill the pool. Please provide additional details to answer this question.

5. To plot the graph of the function y = x^2 - 8|x| + 7, you can use a graphing calculator or graphing software. The graph will be a parabola that opens upwards and has a vertex at the point (0, 7). The graph will also have a "V" shape at the vertex due to the absolute value function.