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