Question

I just need the process of all these pleaseCorrect graph for part b)

Answer 1

Step-by-step explanation:

The given system of inequalities is

-x + 2y > 4

4x + 2y < -2

Then, the lines that separated the regions are -x + 2y = 4 and 4x + 2y = -2.

To graph these lines we need to find two points for each one.

For -x + 2y = 4

If x = 0

-0 + 2y = 4

2y = 4

2y/2 = 4/2

y = 2

If x = 2

-2 + 2y = 4

-2 + 2y + 2 = 4 + 2

2y = 6

2y/2 = 6/2

y = 3

For 4x + 2y = -2

If x = 0

4(0) + 2y = -2

2y = -2

2y/2 = -2/2

y = -1

If x = 1

4(1) + 2y = -2

4 + 2y = -2

4 + 2y - 4 = -2 - 4

2y = -6

2y/2 = -6/2

y = -3

So, we will use the points (0, 2) and (2, 3) for the line -x + 2y = 4 and the points (0, -1) and (1, -3) for the line 4x + 2y = -2. Finally, the graph will be the region above -x + 2y = 4 and the region below 4x + 2y = -2.

Answer:

Therefore, the graph is