Solving a System of Linear
Inequalities
Lesson Plan
Objectives:
- Students will be able to find the
solution area for any system of linear inequalities.
Materials needed:
- Teacher will need 3+ colors of chalk and
blackboard; also straightedge if preferred
- Students will need paper, pencil, and
ruler
Time required:
- Will take up most or all of a 45-minute
class period.
What students should already know how to do:
- how to put equations into slope-intercept
form
- how to graph linear equations
- how to plug points into equations
- what greater than (or equal) and less
than (or equal) means in general
Procedure:
- Explain that solving a system of linear inequalities is similar
to solving a system of linear equations. We graph all the equations as
if they were equal to y, and shade the side of it that is valid for
that particular inequality. Then we find where all the shaded areas
overlap, and that is our solution.
- Write down a system of three linear inequalities such as: x + y ≤ 2, y ≥ -1, and y - 3x
< 3.
- Draw an x-y plane.
- Transform each equation into slope-intercept form by slowing
going through the steps on the board.
- Graph the first equation (in one color) as if it were equal to y.
Determine if the line should be solid or dotted based on the inequality
sign.
- < means y should be under the line and > means y above the
line. With the help of the class, shade (or fringe) the side of the
line y is on. If it's hard to determine, test a point.
- Repeat steps 5 and 6 with the other two equations in two colors
different from the first.
- Determine where all three shaded regions overlap, and this is the
solution area.
- Note that if there is no area where all of the linear
inequalities are satisfied (meaning none of the shaded regions
overlap), then there is NO solution.
Assessment:
- On a test, give the student an x-y plane and a system of linear
inequalities. Have the student draw and find the solution area to the
system.
Extension/homework:
- For homework: Have the student
practice drawing and solving different systems of linear equalities.
Make sure to include some systems that have NO solution.
- Have students use the Applet Solving system of
linear inequalities.
They can access this interactive applet at home and walk through the
steps of the construction on their own to reinforce what they learned
in class and use it to help them on their homework assignment.
Modifications
- Can do the same lesson with students using a projector and Geogebra program.
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Michelle Beckman
beckman.michelle@gmail.com
Updated December 10, 2008.