Question

Знайдіть координати точки перетину графіків функцій у = 2х +4 і у = -4х - 2

Answer 1

Ответ:

система:

{у=2х+4

{у= -4х-2

2х+4= -4х-2

2х+4х= -2-4

6х= -6

х= -1

у=2*(-1)+4= -2+4=2

Ответ: (-1; 2)

Answer 2

Finding the Intersection Point of the Functions

To find the coordinates of the intersection point of the functions \( y = 2x + 4 \) and \( y = -4x - 2 \), we can set the two equations equal to each other and solve for the value of \( x \).

Solving for x

Setting the two equations equal to each other: \[ 2x + 4 = -4x - 2 \]

Adding \( 4x \) to both sides: \[ 6x + 4 = -2 \]

Subtracting 4 from both sides: \[ 6x = -6 \]

Dividing by 6: \[ x = -1 \]

Finding the y-coordinate

Now that we have the value of \( x \), we can find the y-coordinate by substituting \( x = -1 \) into either of the original equations. Let's use \( y = 2x + 4 \) to find the y-coordinate.

Substituting \( x = -1 \) into \( y = 2x + 4 \): \[ y = 2(-1) + 4 \] \[ y = 2 + 4 \] \[ y = 6 \]

Conclusion

Therefore, the coordinates of the intersection point of the functions \( y = 2x + 4 \) and \( y = -4x - 2 \) are (-1, 6).