Question

Y - 2x < 0,3x + y< 3;​

Answer 1

Ответ:

x>y/2

Пошаговое объяснение:

Вычтем

y

из обеих частей неравенства.

−

2

x

<

−

y

Разделим каждый член на

−

2

и упростим.

Answer 2

To graph the system of inequalities Y - 2x < 0 and 3x + Y < 3, we can start by graphing each individual inequality on the same coordinate plane.

First, let's graph Y - 2x < 0. We can rewrite this inequality as Y < 2x, which means that any point below the line Y = 2x satisfies the inequality. We can graph this line by finding two points that satisfy it. For example, when x = 0, we have Y = 0, and when x = 1, we have Y = 2. So we can plot the points (0,0) and (1,2) and draw a line through them:

markdownCopy code
    |              *
    |            * 
    |          * 
    |        * 
    |      * 
    |    * 
    |  *
    |__________________
            x-axis     y-axis

Next, let's graph 3x + Y < 3. We can rewrite this inequality as Y < -3x + 3, which means that any point below the line Y = -3x + 3 satisfies the inequality. We can graph this line in the same way as before. When x = 0, we have Y = 3, and when x = 1, we have Y = 0. So we can plot the points (0,3) and (1,0) and draw a line through them:

markdownCopy code
    |              *
    |            * 
    |          * 
    |        * 
    |      * 
    |    * 
    |  *        *
    |__________________
            x-axis     y-axis

Now we need to shade the region that satisfies both inequalities. One way to do this is to shade the region below the line Y = 2x and above the line Y = -3x + 3:

diffCopy code
    |              *
    |            * 
    |          * 
    |        * 
    |      * 
    |    * 
    |  *=========*   (shaded region)
    |__________________
            x-axis     y-axis

Therefore, the solution to the system of inequalities Y - 2x < 0 and 3x + Y < 3 is the shaded region above the line Y = -3x + 3 and below the line Y = 2x.