Simultaneous Linear Equations

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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.

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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.

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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 :
${\frac {5}{3}}x+y+{\frac {1}{2}}$
$2x+{\frac {1}{2}}y$
${\frac {2}{3}}x+2y+{\frac {5}{2}}$ 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

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