Algebra VIII: solving simultaneous equations (rearrange & substitute)

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Jinhua Mathias

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John Hodkinson	said	Ready to use	8 years, 8 months ago
Luke Park	said	Needs to be tested	8 years, 8 months ago

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John Hodkinson 8 years, 8 months ago

Gave some feedback: Ready to use

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Luke Park 8 years, 8 months ago

Gave some feedback: Needs to be tested

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Luke Park 8 years, 8 months ago

Created this as a copy of Simultaneous equations by substitution 2 with parts.

Name	Status	Author	Last Modified
Simultaneous equations by substitution 2	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 2	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 1	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 1 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 3 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 1 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 2 with parts	Ready to use	joshua boddy	04/02/2021 23:31
Simultaneous equations by elimination 2 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 3	Ready to use	joshua boddy	01/06/2016 09:47
Numerical Skills - Simultaneous equations by elimination 1	Ready to use	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Simultaneous equations by elimination 2	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills - Simultaneous equations by elimination 1 summative	Ready to use	Jinhua Mathias	28/08/2024 12:15
Algebra VIII: solving simultaneous equations (by elimination)	Ready to use	Luke Park	15/09/2016 13:25
Algebra VIII: solving simultaneous equations (rearrange & substitute)	Ready to use	Jinhua Mathias	27/08/2024 16:37
Algebra VIII: solving simultaneous equations (equate & substitute)	Ready to use	Luke Park	08/08/2016 16:16
Algebra VIII: solving Linear equations (rearrange & substitute)	Ready to use	Nasir Firoz Khan	12/08/2016 16:12
Simultaneous equations by elimination	draft	Francis Duah	14/09/2016 12:27
Francis 's copy of Algebra VIII: solving simultaneous equations (equate & substitute)	draft	Francis Duah	14/09/2016 13:04
Hania's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Hania Jasiczak	05/10/2016 14:42
Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Seibu Mary Jacob	18/01/2017 13:42
Jerome's copy of Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Jerome Leary	20/01/2017 22:20
Denis's copy of Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Denis Flynn	11/02/2021 12:04
Algebra VIII: solving simultaneous equations (by elimination)	Ready to use	heike hoffmann	14/11/2018 22:29
Algebra VIII: solving simultaneous equations (equate & substitute)	Ready to use	heike hoffmann	14/11/2018 22:31
Simultaneous equations by elimination 2	draft	Xiaodan Leng	11/07/2019 05:39
Viet's copy of Simultaneous equations by elimination 2	draft	Viet Hoang	13/08/2019 22:23

There are 32 other versions that do you not have access to.

Question statement

Solve the pair of simulatenous equations by working through parts a) to d)

$\begin{eqnarray} \simplify{{n1}*x + {n2}*y} & = & \var{ans1} &&&&&&&(1)\\ \simplify{{n3}*x + {n4}*y} & = & \var{ans2}&&&&&&&(2)\end{eqnarray}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-3
b	integer	-9
ans1	integer	0
ans2	integer	21
ans3	integer	126
yCoef	integer	-14
n1	integer	-6
n2	integer	2
n3	integer	5
n4	integer	-4
n5	rational	21

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-10..10 except 0)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-3

→ Used by:

ans1
ans2
b

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add
Part d) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

We start by rearranging equation (1) like so:

$y =$ Unnamed gap (3)

Advice

We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

We start by rearranging equation (1) like so:

$\simplify{y = 1/{n2}*({ans1}-{n1}*x)}$

$\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) = {ans2}}$

$\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} = {ans2}}$

$\simplify{x=({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})}$

Substitute the value of x back into equation (1) to find

$\simplify{y=({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})}$

Give a worked solution to the whole question.

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Mathematical expression
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Gap-fill
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Algebra VIII: solving simultaneous equations (rearrange & substitute)

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Taxonomy: mathcentre

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John Hodkinson 8 years, 8 months ago

Luke Park 8 years, 8 months ago

Luke Park 8 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Algebra VIII: solving simultaneous equations (rearrange & substitute)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

John Hodkinson 8 years, 8 months ago

Luke Park 8 years, 8 months ago

Luke Park 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`