# Teaching Outlines

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

### Learning objectives

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

### 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

1. State a given problem in algebraic terms
2. Identifying the variables
3. Interpret a linear equation as a line
4. 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 #

• 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 :
${\displaystyle {\frac {5}{3}}x+y+{\frac {1}{2}}}$
${\displaystyle 2x+{\frac {1}{2}}y}$
${\displaystyle {\frac {2}{3}}x+2y+{\frac {5}{2}}}$ When does it becomhttp://karnatakaeducation.org.in/KOER/en/skins/common/images/button_bold.pnge an equilateral triangle?

How to solve

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

Competencies

1. Equilateral triangle must have all sides equal
2. 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
3. Infer that if the sides are same, the expressions must be the same numerical value
4. If that is true, I can use combine the expressions to express one in terms of the other
5. Rearranging terms and combining expressions to form equations
6. Solve

# Math Fun

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