College Algebra (TUTOR DANIEL ONLY)

Module 4 - Home

SYSTEMS OF EQUATIONS AND INEQUALITIES

Modular Learning Outcomes

Upon successful completion of this module, the student will be able to satisfy the following outcomes:

· Case

· Solve systems of equations and inequalities using 3 methods

· Identify system graphs

· Identify types of system solutions

· Graph a system of equations and inequalities on a coordinate plane.

· SLP

· Solve systems of equations and inequalities using 3 methods

· Apply a system to a real world situation

· Write a system of equations.

· Discussion

· Discuss the three methods for solving systems of equations.

Module Overview

Download Module 4 Notes

Methods for Solving Systems of Equations

1) Graphing

Graphing works really well with whole numbers. Fractions and decimals are difficult to graph by hand without the use of a graphing calculator. The graphing method is good if you want to see the graph and identify the solution to the system.

2) Elimination (addition)

This method is used when both equations are in the same format and one of the variables can be eliminated by adding or multiplying.

3) Substitution

This method is used when one of the variables in the equation is isolated and can be substituted into the second equation.

The systems have several possibilities when graphed. They can be:

Consistent: the lines intersect at a single point; one solution

Inconsistent: the lines are parallel and do not intersect; no solution

Dependent: they are exactly the same line; infinitely many solutions

Systems of Inequalities

Systems of inequalities are solved the same way as equations, except they have two unique features. You will choose to connect the points using a dotted or solid line and you will shade above or below the graph.

< and > means it has a dotted line

< and > means it has a solid line

If the line is in slope-intercept form, you can follow the sign for the shading. “Greater than” means you shade above the line and “less than” means you shade below the line. Another option is to test a point. Select any point not on the line. Plug it into the inequality. If it is true, that is the shaded side. False means to shade the other side.

**Please review the following websites for examples of each method, types of solutions, and practice.**

Solve and Graph Systems of Linear Equations - Examples

Stapel, E. (2012). "Systems of linear equations: Definitions.” Purplemath. Retrieved from http://www.purplemath.com/modules/systlin1.htm

Seward, K., & West Texas A&M University. (2011). College algebra tutorial 49: Solving systems of linear equations in two variables. Retrieved from http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut49_systwo.htm

*Go through all sections on the site below*

SparkNotes Editors. (n.d.). SparkNote on Systems of Equations. Retrieved from http://www.sparknotes.com/math/algebra1/systemsofequations/

Spector, L. (2013). Simultaneous linear equations. Retrieved from http://www.themathpage.com/alg/simultaneous-equations.htm

Solve and Graph Systems of Linear Inequalities- Examples

Stapel, E. (2012). "Graphing linear inequalities: y>mx+b, etc.” Purplemath. Retrieved from http://www.purplemath.com/modules/ineqgrph.htm

Seward, K., & West Texas A&M University. (2011). Intermediate algebra tutorial 17: Graphing linear inequalities. Retrieved from http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut17_linearin.htm

SparkNotes Editors. (n.d.). SparkNote on Graphing Inequalities. Retrieved from http://www.sparknotes.com/math/algebra2/inequalities/section1.html

SparkNotes Editors. (n.d.). SparkNote on Solving Systems of Inequalities. Retrieved from http://www.sparknotes.com/math/algebra2/inequalities/section2.rhtml