Simultaneous equations by elimination 2

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Xiaodan Leng

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Xiaodan Leng 5 years, 9 months ago

Created this as a copy of Jinhua's copy of Simultaneous equations by elimination 2.

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
b	integer	-5
ans1	integer	-57
ans2	integer	54
ans3	integer	-75
yCoef	integer	15
n1	integer	-6
n2	integer	3
n3	integer	7
n4	integer	-1

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-10..10 except 0)

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Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

ans1
ans2
b

Advice
"Unnamed part" → "Gap 7." - Correct answer

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add
3. Gap Gap 2. Mathematical expression
  Add
4. Gap Gap 3. Mathematical expression
  Add
5. Gap Gap 4. Mathematical expression
  Add
6. Gap Gap 5. Mathematical expression
  Add
7. Gap Gap 6. Mathematical expression
  Add
8. Gap Gap 7. Mathematical expression
  Add

Gap-fill

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

Solve the pair of equations

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

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. $y = \simplify{{ans1}*{n3}}$

Gap 2. $x +$ Gap 3. $y = \simplify{{ans2}*{n1}}$

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

Gap 4. $\simplify{y = {ans3}}$

Now we can work out $y$

$y =$ Gap 5.

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

$\simplify{{n1}*x}$ + Gap 6. = $\var{ans1}$

which then solves to give $x =$ Gap 7..

Advice

Solve the pair of equations

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

$\simplify{{n3}*{n1}*x + {n3}*{n2}*y = {ans1}*{n3}}$

$\simplify{{n1}*{n3}*x + {n1}*{n4}*y = {ans2}*{n1}}$

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

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

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 $x$ .

$\simplify{{n1}*x + {n2}*{b} = {ans1}}$

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

Give a worked solution to the whole question.

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Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Simultaneous equations by elimination 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`