Solve the system of two linear inequalities graphically. 2y-5x>20 y>-1 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 linear inequalities graphically, we need to graph each inequality separately and then shade the region that satisfies both inequalities.
1. Graph the inequality 2y - 5x > 20:
- We will first find the graph of the equation 2y - 5x = 20 by plotting two points and drawing a straight line through them.
- Let x = 0, then 2y = 20 --> y = 10. So one point is (0, 10).
- Let y = 0, then -5x = 20 --> x = -4. So another point is (-4, 0).
- Plot these points and draw a line through them:
- Now, we will determine which side of the line satisfies the inequality 2y - 5x > 20. Since the inequality is greater than, the region above the line will satisfy the inequality.
2. Graph the inequality y > -1:
- Since this is a simple horizontal line, we just need to determine which side occurs above the line and satisfies y > -1. The region above the line will be shaded.
3. Shade the region that satisfies both inequalities:
- To find the region that satisfies both inequalities, we need to shade the overlapping region between the two lines:
In this case, the region with points that satisfy both inequalities is region D.