Question

Помогите пожалуйста найдите координаты точки пересечения прямых заданных уравнениями:1) х+4у=0 и 2х+3у=25 2) 2х-3у=-2 и 2х+у=10очень нужно

Answer 1

Решение закреплено в файле

Answer 2

Finding the Intersection Points of Two Lines

To find the coordinates of the intersection points of two lines, we can solve the system of equations formed by the given equations. Let's solve each system of equations step by step.

System 1: Equations: 1) x + 4y = 0 2) 2x + 3y = 25

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:

From equation 1, we can express x in terms of y: x = -4y

Substituting this value of x into equation 2: 2(-4y) + 3y = 25 -8y + 3y = 25 -5y = 25 y = -5

Now, substitute the value of y back into equation 1 to find x: x + 4(-5) = 0 x - 20 = 0 x = 20

Therefore, the coordinates of the intersection point for System 1 are (20, -5).

System 2: Equations: 1) 2x - 3y = -2 2) 2x + y = 10

Again, we can use the method of substitution or elimination to solve this system. Let's use the method of substitution:

From equation 2, we can express x in terms of y: x = (10 - y)/2

Substituting this value of x into equation 1: 2((10 - y)/2) - 3y = -2 10 - y - 3y = -2 -4y = -12 y = 3

Now, substitute the value of y back into equation 2 to find x: 2x + 3 = 10 2x = 7 x = 7/2

Therefore, the coordinates of the intersection point for System 2 are (7/2, 3).

To summarize: 1) The coordinates of the intersection point for System 1 are (20, -5). 2) The coordinates of the intersection point for System 2 are (7/2, 3).

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