3.3 - Solve Systems of Linear Inequalities

3.3 - Solve Systems of Linear Inequalities

Objective

To solve systems of linear inequalities

Recall

​The solution to a linear inequality

The set of all points that make the inequality true. This consists of a "half-plane" (a shaded region) and possibly a boundary line.

Example

Example

System of linear inequalities

Each inequality is going to have a shaded region of solutions. For the system, the solution is the overlapping areas of the two shaded regions (or "half-planes")

Example

Multiple Choice

The solution to $$y\ge\frac{1}{2}x-8$$ will have:

• a dotted line, shaded above

• a dotted line, shaded below

• a solid line, shaded above

• a solid line, shaded below

Example

You try

Multiple Choice

Graph the system of inequalities and indicate the solution region.

$$y\le\frac{3}{4}x-4$$

$$y>-7$$

Reminder

We saw during the T-shirt Shop activity Friday that some points will be in the solution region and some will not. What if we don't have a graph? Can we determine if a point is a solution or not?

Yes!

Substitute the x- and y-coordinates into both inequalities. If it makes a true statement for both, that point is a solution.

Try item number 7 on your notes page.

Poll

How do you feel about your ability to solve systems of linear inequalities?

Independent Practice

​Continue to work on items #3-6 on your notes page.