Question

Решите систему уравнений. 1. 3x - 4y = 0 x^2 + y^2 = 25 2. 4xy = 5 3x^2 = 5 3. x^2 = 2 x^2 + xy = 3

Answer 1

Ответ:

я хотел письменно написать но не получилось. Это 100% правильно

Объяснение:

Вот и все × ×

Answer 2

1. To solve the system of equations: 3x - 4y = 0 ...(equation 1) x^2 + y^2 = 25 ...(equation 2)

   We can solve this system by substitution or elimination method. Let's use the elimination method.

   Multiply equation 1 by 3: 9x - 12y = 0 ...(equation 3)

   Now, subtract equation 3 from equation 2: (x^2 + y^2) - (9x - 12y) = 25 - 0 x^2 + y^2 - 9x + 12y = 25

   Rearrange this equation: x^2 - 9x + y^2 + 12y = 25

   Complete the square for x: (x^2 - 9x + 20.25) + y^2 + 12y = 25 + 20.25 (x - 4.5)^2 + y^2 + 12y = 45.25

   Complete the square for y: (x - 4.5)^2 + (y^2 + 12y + 36) = 45.25 + 36 (x - 4.5)^2 + (y + 6)^2 = 81.25

   Now, we have the equation of a circle with center (4.5, -6) and radius sqrt(81.25) = 9.

   Therefore, the solution to the system of equations is all the points (x, y) on the circle with center (4.5, -6) and radius 9.

2. To solve the system of equations: 4xy = 5 ...(equation 1) 3x^2 = 5 ...(equation 2)

   Rearrange equation 1 to solve for y: y = 5 / (4x)

   Substitute this value of y into equation 2: 3x^2 = 5 x^2 = 5 / 3 x = ± sqrt(5/3)

   Substitute the values of x into equation 1 to find y: For x = sqrt(5/3): 4(sqrt(5/3))y = 5 y = 5 / (4sqrt(5/3))

   For x = -sqrt(5/3): 4(-sqrt(5/3))y = 5 y = 5 / (-4sqrt(5/3))

   Therefore, the solutions to the system of equations are: (sqrt(5/3), 5 / (4sqrt(5/3))) and (-sqrt(5/3), 5 / (-4sqrt(5/3)))

3. To solve the system of equations: x^2 = 2 ...(equation 1) x^2 + xy = 3 ...(equation 2)

   Subtract equation 1 from equation 2: (x^2 + xy) - x^2 = 3 - 2 xy = 1

   Substitute this value of xy into equation 1: x^2 = 2 x = ± sqrt(2)

   Substitute the values of x into equation 2 to find y: For x = sqrt(2): (sqrt(2))y = 1 y = 1 / sqrt(2) = sqrt(2) / 2