**Year 10**

**SIMULTANEOUS EQUATIONS**

photo credit Nasa / Goddard Space Flight Center / Reto Stöckli

How old are Xavier and Yvonne?

Y

vonne is twice as old as

X

avier

, and

WE COULD USE "GUESS AND CHECK"

a.k.a. "trial and error"

We need

more elegant

and

reliable

methods

of solving these

kinds of problems ...

BUT this is

not

going to work when the situation becomes more complex!

...if we don't want to be forced to go

back to school

as adults.

Y

vonne is twice as old as

X

avier

, and

Y

vonne is also 3 years older than

X

avier.

BACK TO OUR FUTURE...

How old are Xavier and Yvonne?

If we let

x

= Xavier's age

and let

y

= Yvonne's age

then, we can complete

Step 1

...

STEP 1: TRANSLATE INFORMATION

into math language

Since Yvonne (y) is

twice as old

as Xavier (x),

we can say:

y

= 2

x

Now we have at least four ways available to

solve

these

simultaneous equations

:

1 Trial and Error

2

Graphically

3 By

Substitution

4 By

Elimination

Graphical Solution to Simultaneous Equations

Stop and explore the contents of the following

SATELLITE STATIONS...

Click a content item in a station to zoom in and the back arrow to zoom out, OR pan and use your own zoom.

To Explore:

Solving by SUBSTITUTION

by D.Monahan

Chapter 4A

Chapter 4B

Solving by ELIMINATION

Chapter 3F

basic

intermediate

advanced

Launchpad

One equation with one variable can be solved by

transposition

...

if two unknowns are involved

, we

need a second equation

involving them, and the solution to these

is not often straight-forward...

Simultaneous Equations

Transposing Equations Revision

AVAILABLE Chapter 2D & 2E or click link for a

Powerpoint

how-to...

BUT

However, let's keep it as simple as possible for now...

Self-paced, differentiated sub-unit of Year 10 LINEAR FUNCTIONS UNIT with Distance-Time context emphasis

**about**

Substitution Practice Range

basic

intermediate

advanced

Elimination Practice Range

basic

intermediate

advanced

Prerequiste Knowledge & Skills

Chapter 2A to 2D

or 2E

**Graphical Solutions**

**Solving by Substitution**

**Solving by Elimination**

Revision: Chapter 2A

Substituting into Equations

More Practice? Exercise 3E

More Practice? Exercise 3F

**learning objectives**

Room for Improvement

1. Nest Prezi in Power-point, so animated power-point slides could be used, as well as Prezi.

2. Include some flash animation

3. Improve PPT Slide Content

5. Explore Prezi Add-ons that allow sub-paths in Prezi

After initial introduction to Navigation (Path and Sandpit) in Prezi, Students download a copy or are given viewing rights and explore

Y

vonne is also 3 years older than

X

avier.

These

facts

about Yvonne and Xavier's ages are

true

simultaneously

(i.e. at the same time),

so these

equations are true simultaneously

And, since Yvonne is

3 years older

than Xavier,

we can say:

y

=

x

+3

Applying what you know so far

Intermediate

For ADVANCED Graphical Problems, work through Chapter 4E, 4F & 4G

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/3/Distance%20vs%20Time.%20Linear%20Algebra%20+%20Functions/Substitution%20Worksheet.Basic.docx

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/3/Distance%20vs%20Time.%20Linear%20Algebra%20+%20Functions/Substitution%20Worksheet.Intermediate.docx

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/3/Distance%20vs%20Time.%20Linear%20Algebra%20+%20Functions/Substitution%20Worksheet.Advanced.docx

NB: All hyper-linked documents are stored at end of the following path on qportal:

Home > Student Workspaces > Year 10 > Maths > 05-Calculator > Documents Hyper-linked to Year 10 Simultaneous Eqns PREZI

4. Improve Worksheets in Practice Range - perhaps more Distance-Time orientated

Transposition SkillSheet

then try

Finding x and y intercepts

DOWNLOAD A COPY

https://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/SkillSHEET%203.2%20Intercepts.pdf

DOWNLOAD A COPY:

**Plain Graph Paper**

Download a Copy:

Factorising Quadratics Revision

You might want to brush up on this first!

Powerpoint Talkie

or just check this out:

basic

intermediate

advanced

6. Add Ti-Nspire examples of Solving Sim Eqns

https://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Elimination%20Worksheet.Basic.Word.docx

Steve (the monkey) says...

End of the line...

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Transposing%20Equations.pptx

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/01Z%20Factorising%20Quadratics.ppsx

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/SkillSHEET%204.3%20TRANSPOSING%20EQUATIONS.pdf

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Rules%20Graphs%20and%20Substitution%20TASK%20Word.docx

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/plain%20graph%20paper.pdf

Class Activity

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Revisit%20Taking%20Photographs%20From%20a%20Helicopter-%20Intro%20to%20sub%20method%20CLASS%20ACTIVITY.doc

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Elimination%20Worksheet.Intermediate.docx

Distance/Velocity/Acceleration

NOT FOR THE FAINT HEARTED

COMING SOON...

1. Estimating Velocity by drawing tangents to Distance-Time curves and finding their gradients.

2. Similarly for Acceleration from Velocity-Time Graphs

3. Link to Linemotion Applet

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/linemotion.zip

Solve as best you can...

Two wombats start at the same time on opposite sides of a rectangular paddock. One is faster than the other. They cross at a point 720 metres from the left side on their way to the other end. When each reaches the other side it stops and eats for 11.5 minutes. The wombats meet again at a point 400 metres from the right side of the paddock.

If p = speed of the wombat starting from left,

q = speed of the wombat starting from right, and

x = width of the paddock

How wide is the paddock?

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/Elimination%20Worksheet.Advanced.docx

PIGS IN SPACE

Or, test your skills at

solving basic equations

basic

intermediate

advanced

The different uses of

the Cartesian Plane

Test your understanding

http://www.sycd.co.uk/dtg/

http://qportal.kew.vic.edu.au/virtualclass/y10/maths/5/Documents%20Hyper-linked%20to%20Year%2010%20Simultaneous%20Eqns%20PREZI/xy%20vs%20dt%20graphs.docx

Link to WORD Doc form

ANSWERS

You will know what SIMULTANEOUS EQUATIONS are

You will be reminded how to solve them graphically

You will know TWO ways to solve them algebraically