Question

Найдите коррдинаты точек пересечения прямых,заданных уровнениями y=-4х+3 и y=1/2x + 3 y=-2х-10 и у=-х-7 ПОМОГИТЕ СРОЧНО ПЛИИИИЗ!!!!!

Answer 1

Y = -4*x + 3 и y = 0.5*x + 3

-4*x + 3 = 0.5*x + 3
x = 0, y = 3
Ответ: (0; 3)

y = -2*x - 10 и y = -x - 7
-2*x - 10 = -x - 7
x = -3, y = - 4
Ответ: (-3; -4)

Answer 2

Coordinates of Intersection Points of Given Lines

To find the coordinates of the intersection points of the given lines, we can solve the systems of equations formed by the pairs of linear equations.

For the first pair of equations: 1. \( y = -4x + 3 \) 2. \( y = \frac{1}{2}x + 3 \)

We can solve for the intersection point by setting the two equations equal to each other: \[ -4x + 3 = \frac{1}{2}x + 3 \]

Solving for \( x \): \[ -4x - \frac{1}{2}x = 3 - 3 \] \[ -\frac{9}{2}x = 0 \] \[ x = 0 \]

Substituting \( x = 0 \) into either of the original equations gives us the value of \( y \): \[ y = -4(0) + 3 \] \[ y = 3 \]

So, the first pair of equations intersect at the point (0, 3).

For the second pair of equations: 1. \( y = -2x - 10 \) 2. \( y = -x - 7 \)

We can solve for the intersection point by setting the two equations equal to each other: \[ -2x - 10 = -x - 7 \]

Solving for \( x \): \[ -2x + x = -7 + 10 \] \[ -x = 3 \] \[ x = -3 \]

Substituting \( x = -3 \) into either of the original equations gives us the value of \( y \): \[ y = -2(-3) - 10 \] \[ y = 6 - 10 \] \[ y = -4 \]

So, the second pair of equations intersect at the point (-3, -4).

Therefore, the coordinates of the intersection points are: 1. For the first pair of equations: (0, 3) 2. For the second pair of equations: (-3, -4)