Question

23.5. Найдите координаты точек пересечения графиков функций: 1) у = -6х +1 и y = 5х + 9; 2) у = -17 + 3,4х иу=-1,2х + 69; 3) у = 21 – 9х и у = -2,5х + 8; 4) y = 16,2 + 8х иу = -0,8х + 7,4; 5) y = 1 – 3х и у=-х – 1; 6) y = 1 + 7х иу = 6,5х. Помогите пожалуйста. СРОЧНО!!!

Answer 1

нужно решить шесть систем.

1) приравняем у, получим  -6х +1= 5х + 9; 11х=-88; х=-8/11; у=(48/11)+1=59/11=

5 4/11

Ответ (-8/11; 5 4/11)

2)  -17 + 3,4х=-1,2х + 69; 4,6х=86; х=860/46=18  16/23; у=-1.2*16/23+69=

15678/115=68 16/115

Ответ (18 16/23; 68 16/115)

3) 21-9х=-2.5х+8; 13=6.5х; х=2; у=21-9*2=21-18=3

Ответ (2;3)

4) 16,2 + 8х = -0,8х + 7,4; 8.8х= 8.8; х=1; у=16.2+8=24.2

Ответ (1; 24.2)

5) 1 – 3х =-х – 1;2=2х;  х=1; у=1-3*1=-2

Ответ (1; -2)

6)  1 + 7х = 6,5х;  0.5х=-1; х=-2; у=1+(-2)*7=-13

Ответ (-2;-13)

Answer 2

23.5. Найдите координаты точек пересечения графиков функций:

1) y = -6x + 1 и y = 5x + 9 2) y = -17 + 3.4x и y = -1.2x + 69 3) y = 21 - 9x и y = -2.5x + 8 4) y = 16.2 + 8x и y = -0.8x + 7.4 5) y = 1 - 3x и y = -x - 1 6) y = 1 + 7x и y = 6.5x

1) y = -6x + 1 и y = 5x + 9:

To find the coordinates of the intersection point between these two functions, we need to set them equal to each other and solve for x:

-6x + 1 = 5x + 9

Simplifying the equation:

-11x = 8

Dividing both sides by -11:

x = -8/11

Now, we can substitute this value of x into either of the original equations to find the corresponding y-coordinate. Let's use the first equation:

y = -6(-8/11) + 1

Simplifying:

y = 48/11 + 1

y = 48/11 + 11/11

y = 59/11

Therefore, the coordinates of the intersection point are approximately (-8/11, 59/11).

2) y = -17 + 3.4x и y = -1.2x + 69:

Setting the two equations equal to each other:

-17 + 3.4x = -1.2x + 69

Simplifying:

4.6x = 86

Dividing both sides by 4.6:

x = 86/4.6

x ≈ 18.7

Substituting this value of x into either of the original equations:

y = -17 + 3.4(18.7)

y ≈ -17 + 63.58

y ≈ 46.58

Therefore, the coordinates of the intersection point are approximately (18.7, 46.58).

3) y = 21 - 9x и y = -2.5x + 8:

Setting the two equations equal to each other:

21 - 9x = -2.5x + 8

Simplifying:

6.5x = 13

Dividing both sides by 6.5:

x = 13/6.5

x = 2

Substituting this value of x into either of the original equations:

y = 21 - 9(2)

y = 21 - 18

y = 3

Therefore, the coordinates of the intersection point are (2, 3).

4) y = 16.2 + 8x и y = -0.8x + 7.4:

Setting the two equations equal to each other:

16.2 + 8x = -0.8x + 7.4

Simplifying:

8.8x = -8.8

Dividing both sides by 8.8:

x = -1

Substituting this value of x into either of the original equations:

y = 16.2 + 8(-1)

y = 16.2 - 8

y = 8.2

Therefore, the coordinates of the intersection point are (-1, 8.2).

5) y = 1 - 3x и y = -x - 1:

Setting the two equations equal to each other:

1 - 3x = -x - 1

Simplifying:

-2x = -2

Dividing both sides by -2:

x = 1

Substituting this value of x into either of the original equations:

y = 1 - 3(1)

y = 1 - 3

y = -2

Therefore, the coordinates of the intersection point are (1, -2).

6) y = 1 + 7x и y = 6.5x:

Setting the two equations equal to each other:

1 + 7x = 6.5x

Simplifying:

0.5x = -1

Dividing both sides by 0.5:

x = -2

Substituting this value of x into either of the original equations:

y = 1 + 7(-2)

y = 1 - 14

y = -13

Therefore, the coordinates of the intersection point are (-2, -13).

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