# Simultaneous Linear Equations

From Karnataka Open Educational Resources

Philosophy of Mathematics |

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## Contents

# Concept Map

# Textbook

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# Additional Information

## Useful websites

## Reference Books

# Teaching Outlines

## Concept #1 - Where do I use simultaenous equations

### Learning objectives

- There are two quantities/ parameters that are used together to describe something.
- This is of the forms ax+by = c
- You need two sets of equations to find the solutions.
- Extend this understanding for different sets of variables.

### Notes for teachers

### Activity No #

- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner

### Activity No #

- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner

## Concept #2 - Graphical Method of Simultaneous Equations

### Learning objectives

- State a given problem in algebraic terms
- Identifying the variables
- Interpret a linear equation as a line
- Understand that the solution is a point on both the lines, they intersect

### Notes for teachers

It is better to use the graphical method before the algebraic manipulation.

### Activity No 1: Simultaneous linear equation

### Activity No #

- Estimated Time
- Materials/ Resources needed
- Prerequisites/Instructions, if any
- Multimedia resources
- Website interactives/ links/ / Geogebra Applets
- Process/ Developmental Questions
- Evaluation
- Question Corner

# Hints for difficult problems

## Applications of Simultaneous Linear Equations - Exercise 3.5.5

### Problem #5, Exercise 3.5.5, Page 213

The measure of the sides (in cms) of a triangle are :

'"`UNIQ--postMath-00000001-QINU`"'

'"`UNIQ--postMath-00000002-QINU`"'

'"`UNIQ--postMath-00000003-QINU`"'
When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle?

**How to solve**

- These are measurements of the sides of the triangle
- Equate the three
- Substitute and solve for x and y.

**Competencies**

- Equilateral triangle must have all sides equal
- The sides of a triangle are line (segments) and can be expressed as a linear equation. Though this is not used for solving this problem
- Infer that if the sides are same, the expressions must be the same numerical value
- If that is true, I can use combine the expressions to express one in terms of the other
- Rearranging terms and combining expressions to form equations
- Solve

# Project Ideas

# Math Fun

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