Solve the system of two linear inequalities graphically.
{y≤6x−9 y>−2x+3
Find the region with points that satisfy both inequalities. Select the region you wish to be shaded A, B, C or D
To solve this system of inequalities graphically, we first need to graph the lines represented by the inequalities.
1. Graph the line y = 6x - 9:
- Plot two points on the line. For example, when x = 0, y = -9, and when x = 2, y = 3.
- Draw a line passing through these two points.
2. Graph the line y = -2x + 3:
- Plot two points on the line. For example, when x = 0, y = 3, and when x = 2, y = -1.
- Draw a line passing through these two points.
Now, we need to identify the region that satisfies both inequalities.
3. Shade the area below the line y = 6x - 9 since the inequality is y ≤ 6x - 9.
4. Shade the area above the line y = -2x + 3 since the inequality is y > -2x + 3.
The shaded region where the two shaded areas overlap represents the region that satisfies both inequalities. Let's label the regions:
A: Shaded area below the line y = 6x - 9
B: Shaded area above the line y = -2x + 3
The region we wish to be shaded is C, which is the intersection of regions A and B.