Algebra VIII: solving simultaneous equations (by elimination)

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Created this as a copy of Algebra VIII: solving simultaneous equations (by elimination).

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 simultaneous equations by working through parts a) to e)

$\begin{eqnarray} \simplify{{n1}*x + {n2}*y -{ans1}} = 0 &&&&&&&(1)\\ \simplify{{n3}*x + {n4}*y -{ans2}} = 0 &&&&&&&(2)\end{eqnarray}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	5
b	integer	3
ans1	integer	-60
ans2	integer	-23
ans3	integer	213
yCoef	integer	71
n1	integer	-9
n2	integer	-5
n3	integer	-7
n4	integer	4

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Name

Data type

Value

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random(-10..10 except 0)

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Description

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Generated value: `integer`

→ Used by:

ans1
ans2
b

Advice
"Part e)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
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
Part e) 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 $y$ first. To do this, we need to eliminate $x$ from the equations. The quickest way to do this is to multiply the first equation by the co-efficient of $x$ in the second equation (here $\var{n3}$ ), and multiply the second equation by the co-efficient of $x$ in the first equation (here $\var{n1}$ ). We then get the equations:

Gap 0. $x$ + Gap 1. $\simplify{y +{ans1}*(-1)*{n3}} = 0$

Gap 2. $x$ + Gap 3. $\simplify{y +{ans2}*(-1)*{n1}} = 0$

Advice

Solve the pair of equations

$\begin{eqnarray} \simplify{{n1}*x + {n2}*y -{ans1}} = 0 &&&&&&&(1)\\ \simplify{{n3}*x + {n4}*y -{ans2}} = 0 &&&&&&&(2)\end{eqnarray}$

$\simplify{{n3}*{n1}*x + {n3}*{n2}*y +{ans1}*(-1)*{n3}} = 0$

$\simplify{{n1}*{n3}*x + {n1}*{n4}*y +{ans2}*(-1)*{n1}} = 0$

We then subtract one new equation from the other to get:

$\simplify{{yCoef}y - {ans3} = 0}$

Now we can work out $y$

$y = \var{b}$

and substitute this value back in to any of the previous equations to get the value for $x$ .

$\simplify{{n1}*x + {n2}*{b} + (-1)*{ans1}}$ = 0

which then solves to give $x = \var{a}$ .

Give a worked solution to the whole question.

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This question is used in the following exam:

Construction Engineering Outcome 3 by Sandra Ferguson in Sandra's workspace.

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Algebra VIII: solving simultaneous equations (by elimination)

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heike hoffmann 6 years, 5 months ago

heike hoffmann 6 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Algebra VIII: solving simultaneous equations (by elimination)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

heike hoffmann 6 years, 5 months ago

heike hoffmann 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`