Question

Решите систему уравнений (графически) x-2y=6 6x-2y=8

Answer 1

X-2y=6  2y=x-6  y=0.5x-3
6x-2y=8   3x-y=4    y=3x-4
по графику прямые пересекаются в точке х=0,4  у=-2,8

Answer 2

Graphical Solution to the System of Equations

To solve the system of equations graphically, we will plot the given equations on a coordinate plane and find the point of intersection, if it exists. The point of intersection represents the solution to the system.

The given system of equations is:

Equation 1: x - 2y = 6 Equation 2: 6x - 2y = 8

Let's solve it step by step:

Step 1: Convert the equations to slope-intercept form (y = mx + b).

For Equation 1: x - 2y = 6 => -2y = -x + 6 => y = (1/2)x - 3

For Equation 2: 6x - 2y = 8 => -2y = -6x + 8 => y = 3x - 4

Step 2: Plot the equations on a coordinate plane.

We will create a graph by plotting points for each equation. To simplify, we will plot a few points and draw a straight line through them.

Equation 1: y = (1/2)x - 3 Let's choose a few x-values and find the corresponding y-values: For x = 0, y = -3 For x = 2, y = -2 For x = 4, y = -1

Plotting these points, we get a line:

   |
 -3|            *
   |        *
   |    *
   |*   
   +-------------------
    0   2   4   6   8   x

Equation 2: y = 3x - 4 Similarly, let's choose a few x-values and find the corresponding y-values: For x = 0, y = -4 For x = 2, y = 2 For x = 4, y = 8

Plotting these points, we get another line:

   |
 -3|            
   |        *     
   |    *    
   |*   
   +-------------------
    0   2   4   6   8   x

Step 3: Find the point of intersection.

Looking at the graph, we can see that the two lines intersect at a single point. This point represents the solution to the system of equations.

   |
 -3|            
   |        *     
   |    *    * (2, -1)
   |*   
   +-------------------
    0   2   4   6   8   x

Therefore, the solution to the given system of equations is x = 2 and y = -1.