How do you graph the system #y ≥ - 5# and #y ≤ 2x + 5# and #y ≤ -2x + 5#?

For graphing the system, first graph the lines y= -5, y= 2x+5 and y= -2x+5 in usual manner.

y>= -5 would represent the region lying above y= -5, y<= 2x+5 would represent the region to the left of y=2x+5 and y<= -2x+5 would represent the region to the right of y= -2x+5. This can be easily verified by observing the location of point (0,0) which satisfies all the three inequalities.

The region represented by the system would be the region common to all of them. This would be a triangular region bounded by the three lines. These lines would also be part of the common region. To highlight the region, it can be shaded to distinguish it from rest of the region.

To graph the system of inequalities y ≥ -5, y ≤ 2x + 5, and y ≤ -2x + 5, you would start by graphing the boundary lines for each inequality.

1. For y ≥ -5, you would draw a horizontal line at y = -5, which is a solid line since the inequality includes equality.
2. For y ≤ 2x + 5, you would graph the line y = 2x + 5, making it a solid line since the inequality includes equality.
3. For y ≤ -2x + 5, you would graph the line y = -2x + 5, also as a solid line.

Next, you would shade the regions that satisfy each inequality:

• For y ≥ -5, you would shade above the horizontal line.
• For y ≤ 2x + 5, you would shade below the line.
• For y ≤ -2x + 5, you would also shade below the line.

The region where all three shaded regions overlap represents the solution to the system of inequalities.