3.3+Graph+Systems+of+Linear+Inequalities


 * A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system. **

If you need help solving inequalities, refer back to page 1.6

First, you graph the system of inequalities.
 * 1)** y > -3x+5
 * 2) ** y ≤ x-2

If the inequality is **LESS THAN OR EQUAL TO** or **GREATER THAN OR EQUAL TO**, the line is drawn as a solid line. If the inequality is simply **LESS THAN** or **GREATER THAN**, the line is drawn as a dashed line.

**You can determine where to shade the inequality two different ways**: If the sign is less than or less than/equal to (< or __ < __ ), the shading will occur below the graphed line
 * If the sign is greater than or greater than/equal to ( > or __ > __ ), the shading will occur above the graphed inequality line.

Choose a point not on the line and see if it makes the inequality true. If the inequality is true, you will shade THAT side of the line -- thus shading OVER the point. If it is false, you will shade the OTHER side of the line -- not shading OVER the point. **If a line does not go through the point (0,0), use that point to find out where to shade! It's the easiest.**
 * Test Point Method:

Example: **y > -3x + 5**

Plug (0,0) in for the x and y in the inequality. (0) > -3(0) +5 0 > 5



Then you identify the region that is common to both graphs, which is where the shading of both inequalities overlap each other. In the picture above, the color of the overlapping shades is purple.

media type="custom" key="23791004" If you graph the systems and there is no overlapping space when you shade the inequality, that is simply a graph with no solution. An example is shown:

Lastly, some linear inequalities that you graph will have absolute values in the inequality (e.i. y > |x+4|). All absolute value graphs will plot a line that will look like a 'V', as shown: Let's say the inequality you get is y > |x|. Your table to do before graphing would look like this: (The graph of this table is the one seen above.) Creating tables will help you graph the inequalities/make it much easier. If you're having trouble figuring out how to solve an absolute inequality, such as y < |x+4|, first make a table. Fill in the x values on the table. Then, plug those x values you chose in the inequality, and solve.
 * X || -2 || -1 || 0 || 1 || 2 ||
 * Y || 2 || 1 || 0 || 1 || 2 ||

Ex: x = -1 y < |(-1)+4)| y < |3| y < 3

The shading of the absolute value inequalities is the same as shading for regular inequalities.

Assessment:




 * This flash animation can show you how to do this chapter, and more! Check it out if you can!**