Solve the system of two linear inequalities graphically.
{x>2 y≥2 Find the region with points that satisfy both inequalities. Select the region you wish to be shaded A, B, C or d
To solve the system of two linear inequalities graphically, we start by graphing each inequality on the xy-plane and then find the region where both inequalities are satisfied.
1) x > 2:
To graph x > 2, we draw a vertical dashed line passing through x = 2 and shade the region to the right of the line (excluding the line itself).
2) y ≥ 2:
To graph y ≥ 2, we draw a horizontal solid line passing through y = 2 and shade the region above the line (including the line itself).
The region where both inequalities are satisfied is the shaded region (C) where the shaded region to the right of x = 2 intersects with the shaded region above y = 2.
Here is a visual representation of the solution:
```
^ y
|
|
C | ┆ -
| ┆
B | ┆ ┏━┓
| ┆ ┃ ┃
A |───┅┆───┃ ┃
| ┆ ┃ ┃
d | ┆ ┖━┛
| ┆
-5|───┆──┆──┆──
-5 0 5 10 15 20 x
```
So the region with points that satisfy both inequalities is represented by the shaded region labeled C.