Course: Algebra II / 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 2x2 or higher 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:
- 5.5.1 Translate application problems into 2x2 or 3x3 linear systems, particularly mixture problems
- 5.5.2 Electronically solve the system and recognize the solutions significance in terms of the original application which the system modeled
Terminology
Define: mixture problem, quantity and quality( in terms of mixture problems)
Text Notes
Text:
Intro & Inter Algebra for CS 3ed by Blitzer, sect. 4.4
- The mixture problems are particularly important. The number/money problems are useful too.
- SKIP the motion (D=RT) problems. These are covered in math 093/095.
- Concentrate on translating the word problem into a system of linear equations. You may then solve it electronically :)