Question

X+y=0 -x+2y=6 графическим способом

Answer 1

Из уравнения x + y = 0 выражаем:
y = -x
Из уравнения 2y - x = 6 выражаем:
y = (6 + x)/2
Строим график этих двух функций, и как видим из графика точка пересечения функций находится в координате (-2; 3).
Понятно, что решением системы и будут значения x = -2; y = 3.

Answer 2

To solve the system of equations graphically, we need to plot the lines represented by each equation on the same coordinate system. The point of intersection of the two lines will be the solution to the system of equations.

Let's first rewrite the equations in the form "y = mx + b" (slope-intercept form) to identify their slopes and y-intercepts:

Equation 1: x + y = 0 y = -x + 0 y = -x

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

Now, let's plot these two lines on the graph:

Graph of y = -x (line 1):

• Let's calculate some points for line 1: For x = -2, y = 2 For x = 0, y = 0 For x = 2, y = -2

Graph of y = (1/2)x + 3 (line 2):

• Let's calculate some points for line 2: For x = -4, y = 1 For x = 0, y = 3 For x = 4, y = 5

Now, let's plot these points and draw the lines:

(Plotting the graph here is challenging due to the text-based interface. However, you can easily do it on paper or using graphing software.)

The lines will intersect at a specific point, which is the solution to the system of equations. If the lines are parallel and do not intersect, it means there is no solution (inconsistent system). If the two lines overlap each other, it means there are infinite solutions (consistent and dependent system).

Based on the equations, the lines are not parallel, and they intersect at a single point, which means there is a unique solution to the system of equations.

You can find the coordinates of the intersection point by solving the two equations simultaneously:

x + y = 0 -x + 2y = 6

Add the equations: 3y = 6 y = 2

Now substitute the value of y into one of the equations to find x: x + y = 0 x + 2 = 0 x = -2

So, the solution to the system of equations is x = -2 and y = 2.