Name
Algebra 1 Extension Menu
Writing Linear Systems and Systems of Inequalities
Choose a learning activity from one square to complete. If you choose the square, “Write your idea here,” please see the teacher with your idea first.
Circle the number of the learning activity you choose.
Turn in this paper with your work.
1. When a system with three or more linear inequalities is graphed, polygons can be formed.
Think about and describe what regions formed by the intersection of nonlinear inequalities would look like.
4 . Use the “Solving Systems with Matrices” worksheet to learn how to solve a system of linear equations using matrices.
If you are not familiar with entering and using matrices on the graphing calculator, visit the website http://mathbits.com/mathbits/TI
Section/Precalculus/matrices.ht
m
2. Write three different systems that each have a solution of x=8 and y=22. One system should be appropriate for solving using graphing, one for solving using substitution, and the last for solving using combinations (elimination).
Optional Challenge: For each system that you write, design a real life situation that could be modeled by that system.
5. Complete the 7-5
Enrichment worksheet by writing systems of inequalities to represent each shaded region.
On a coordinate plane, create your own shaded region and write the system of inequalities represented by it.
3. Design a brochure or foldable to explain three different methods that can be used to solve a system of equations. Include details about what types of systems or situations are best solved using those methods.
6.
Algebra 1/Linear Systems and Systems of Inequalities

Concept and/or Topic: Linear Systems and Systems of Inequalities
Intended Purpose: Culminating activity for the unit or alternative activity for students who have mastered curricular indicators.
Standards:
ALG.05
Analyze a wide variety of patterns and functional relationships using the language of
ALG.10
ALG.15
ALG.20
mathematics and appropriate technology expressed numerically, algebraically, and geometrically.
Model and interpret real-world situations, using the language of mathematics and appropriate technology.
Collect, organize, analyze, and present data.
Apply the basic concepts of statistics and probability to predict possible outcomes of realworld situations 3.2.
Indicators Addressed:
Box 1: Topic Covered: Graphing Systems of Linear Inequalities
Box 2: Topic Covered: Set-up and solve Real world problems
Box 3: MA.ALG.10.55 Solve a system of two linear equations algebraically and graphically, including parallel, intersecting, and same lines (1.2.3, TA)
Box 4: MA.ALG.10.55 Solve a system of two linear equations algebraically and graphically, including parallel, intersecting, and same lines (1.2.3, TA)
Topic extension- Using matrices to solve systems.
Box 5: Topic Covered: Graphing Systems of Linear Inequalities
Organizational Tips:
Box 3: Information about foldables can be found in your Glencoe resource kit.
Box 4: Duplicate the Solving Systems with Matrices handout and make available for students.
Box 5: Duplicate the 7-5 Enrichment handout from your Glencoe Resource kit and make available for students.
Algebra 1/Linear Systems and Systems of Inequalities

Solving Systems with Matrices
The beginning of matrices and determinants goes back to the second century BC although traces can be seen back to the fourth century BC. However, it was not until near the end of the 17 th century that the ideas reappeared and development really got underway.
It is not surprising that the beginning of matrices should arise through the study of systems of linear equations. The Babylonians studied problems which led to simultaneous linear equations and some of these are preserved in clay tablets which survive. For example a tablet dating from around 300 BC contains the following problem:-
There are two fields whose total area is 1800 square yards. One produces grain at the rate of
2
/
3 of a bushel per square yard while the other produces grain at the rate of 1 /
2
a bushel per square yard. If the total yield is 1100 bushels, what is the size of each field.
The Chinese, between 200 BC and 300 BC, came much closer to matrices than the Babylonians. Indeed, it is fair to say that the text Nine Chapters of the Mathematical Art written during the Han Dynasty gives the first known example of matrix methods.
Source: http://turnbull.mcs.stand.ac.uk/~history/HistTopics/Matrices_and_determinants.html
To solve a system of linear equations using matrices, you can multiply the inverse of the coefficient matrix by the constant matrix.
____________________________________________________________________________________
System of Linear Equations ax
 cx

 by dy

 e f
Coefficient Matrix

 a c b d


Constant Matrix

 f e



 a c
Solution to the system:
-1 b d



 f e


Algebra 1/Linear Systems and Systems of Inequalities