Solve the system of two linear inequalities graphically. y<6 y>=2 Find the region with points that satisfy both inequalities. Select the region you wish to be shaded: A, B or C,
To solve the system of two linear inequalities graphically, we can start by graphing each inequality individually and then identifying the region that satisfies both inequalities.
The first inequality, y < 6, represents a horizontal line that goes through y = 6 but does not include the line itself. Therefore, we can graph this inequality as a dashed line (to indicate that points on the line are not included) below y = 6.
The second inequality, y >= 2, represents a horizontal line starting from y = 2 and including all points above it. Thus, we can graph this inequality as a solid line (to indicate that points on the line are included) starting from y = 2 and extending upwards.
By graphing both inequalities on the same coordinate plane, we are left with the region that satisfies both inequalities. We can select the shaded region that satisfies both inequalities, which in this case is region C.
Here is a graphical representation of the solution:
```
| C
6 |-----------------------
| |
| |
2 |-----------------------
|
-------------------------
x-axis
```
Region C represents all the points where y is strictly less than 6 (below the dashed line) and greater than or equal to 2 (above the solid line).
Therefore, region C is the shaded region that satisfies both inequalities.