Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Linear Systems
Subtopic: Applications

Overview

In real world problems there are often several constraints (conditions on the variables) that need to be met simultaneously. For instance when designing a plane at Boeing the engineers typically work with systems containing 140,000 equations in 140,000 variables! (Thank goodness for technology, aye?)

The applications on which we will concentrate here are mostly mixture problems meaning that two or more things (nuts, coffees, etc.) are being mixed together. When translating them into a linear system, look for the "quantity * quality" relationship as it will help you to form the equations.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.4.1 Translate application problems into 2x2 (and possibly 3x3) linear systems, particularly mixture problems
• 5.4.2 Solve the system and recognize the solutions significance in terms of the original application which the system modeled

Terminology

Terms you should be able to define: mixture problem, quantity and quality (in terms of mixture problems)

Text Notes

• The mixture problems are particularly important. The number/money problems are useful too.
• SKIP the motion (D=RT) problems. These are covered in a future algebra course.
• SKIP any examples/exercises covering "supply and demand", "curve fitting", or "linear regression".
• Concentrate on translating the word problem into a system of linear equations. You may then solve it electronically :)