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How do you graph the system of linear inequalities #y>=-x#, #y>=0#, and #<0#?

Answer 1

Eli Assouline

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Answer 2

Jace Anderson

To graph the system of linear inequalities:

Graph the boundary lines for each inequality separately:
- For (y \geq -x), draw the line (y = -x) as a solid line.
- For (y \geq 0), draw the horizontal line (y = 0) as a solid line.
- For (y < 0), draw the horizontal line (y = 0) as a dashed line.
Shade the regions that satisfy each inequality:
- For (y \geq -x), shade the region above the line.
- For (y \geq 0), shade the region above the line (including the line itself).
- For (y < 0), shade the region below the dashed line.
The solution to the system of inequalities is the overlapping shaded region where all three conditions are met.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph the system of linear inequalities #y&gt;=-x#, #y&gt;=0#, and #&lt;0#?

How do you graph the system of linear inequalities #y>=-x#, #y>=0#, and #<0#?