Equations Reducible To The Linear Form
Chapter Name : Linear Equations In One Variable |
Sub Topic Code : 104_08_02_07_01 |
Topic Name : Equations Reducible To The Linear Form |
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Sub Topic Name : Equations Reducible To The Linear Form |
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Introduction
In many problems like the upstream and downstream travel in boat, the unknowns fall into denominator. In such situations, substitutions are made and the equation solved as a normal linear equation.
Pre-Requisites:
Basic knowledge about arithmetic operations and linear equations
Activity:
The distance is equal. One destination can be defined by a linear expression and the other by another expression. By equating these two expressions, we get the unit distance.
Real Life Question:
The speed of a boat in a river depends on the speed of the flowing water and also the direction of traverse ( up stream/ down stream). How do we know the actual speed of boat?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Linear Equation | The power of the variable should be 1 |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Map | On a map, set destinations and a unit distance. For destinations at equal distances make different routes and equate them. |
Real life uses :
Conversion of units from one scale to other, exchange rates, travelling, telephone tarrif
Practical examples around us
| Examples | Explainations |
|---|---|
| Money Exchangers | USD= 55.4*INR (Changes everyday) |
| Cell phone tarrif | The seconds plan in the prepaid sim can be calculated as rate = 1.2 x time in seconds. Here rate is the variable, and we know how long we spoke. |
What you learn in Theory:
An Intro on methods to reduce nonlinear equations into linear equations.
What you learn in Practice:
For a nonlinear equations, cross multiplying would transform it into linear equation with expressions on both sides. This has many applications in applied science and commerce.