Question

СРОЧНО x+2y=4 2x+3y=7 Рішити графічним методом

Answer 1

Ответ:

x=2, y=1

Объяснение:

x+2y=4

2x+3y=7

x+y=3

y=1

x+2*1=4

x=2

Answer 2

Problem Statement

We are given the following system of equations: ``` x + 2y = 4 2x + 3y = 7 ``` We need to solve this system of equations using the graphical method.

Graphical Method

To solve the system of equations graphically, we will plot the lines represented by each equation on a coordinate plane and find the point of intersection, which represents the solution to the system.

Let's start by rearranging the equations in slope-intercept form (y = mx + b): ``` x + 2y = 4 => 2y = -x + 4 => y = (-1/2)x + 2 2x + 3y = 7 => 3y = -2x + 7 => y = (-2/3)x + 7/3 ```

Now, we can plot the lines on a coordinate plane:

Line 1: y = (-1/2)x + 2 - Choose some x-values and calculate the corresponding y-values: - When x = 0, y = 2 - When x = 2, y = 1 - Plot the points (0, 2) and (2, 1), and draw a line passing through them.

Line 2: y = (-2/3)x + 7/3 - Choose some x-values and calculate the corresponding y-values: - When x = 0, y = 7/3 - When x = 3, y = 5/3 - Plot the points (0, 7/3) and (3, 5/3), and draw a line passing through them.

The graph should look like this:


From the graph, we can see that the lines intersect at the point (3, 1). Therefore, the solution to the system of equations is x = 3 and y = 1.

Conclusion

The solution to the given system of equations, obtained using the graphical method, is x = 3 and y = 1.