How do you graph the system of linear inequalities?

Answer 1

Graphing an inequality such as y > mx + b is similar to graphing the equation y = mx + b, with a couple of differences:

1. Since it is not equal, you draw a dashed line, rather than a solid line.
2. If y is greater than: shade the area above the dashed line; less than: shade below the dashed line.

Since it's a system of linear inequalities, you will wind up with different shaded areas which overlap, creating a bounded area.

These types of problems usually come from some sort of real-world situation, such as finding optimum products from limited resources. Example is a farmer has a fixed number of acres to plant (or can use for cattle grazing, instead). Some crops grow faster than others, so time in-season is a limiting factor. Other things, such as money (how much to be spent on seed, watering, fertilizer, people or equipment to harvest, etc.)

The areas which overlap represent the scenarios which are possible with the given resources. Then you can look at the graph and figure out where there is a maximum profit for example.