Simultaneous Equations

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Gareth Woods

History

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Gareth Woods 8 years ago

Created this as a copy of Gareth's copy of Denis's copy of Simultaneous equations (2).

Name	Status	Author	Last Modified
Simultaneous linear equations (variables)	Ready to use	Bill Foster	01/06/2016 09:47
Jessica's copy of Simultaneous linear equations (variables)	Ready to use	Jessica Ryan	01/06/2016 09:47
Lois's copy of Simultaneous linear equations (variables)	Ready to use	Lois Rollings	20/09/2016 12:50
José's copy of Lois's copy of Simultaneous linear equations (variables)	Ready to use	Jos Klenner	02/12/2020 15:42
Systems of linear equations in 2 variables	draft	Vicky Hall	06/02/2018 16:00
Simultaneous linear equations (variables)	draft	steve kilgallon	05/09/2016 11:50
John's copy of Simultaneous linear equations (variables)	draft	John Bridges	05/09/2016 13:02
Mock exam Simultaneous linear equations (variables)	draft	steve kilgallon	27/10/2016 19:36
Simultaneous equations (2)	draft	Hannah Bartholomew	15/09/2017 15:26
Denis's copy of Simultaneous equations (2)	draft	Denis Flynn	11/02/2021 12:04
Gareth's copy of Denis's copy of Simultaneous equations (2)	draft	Gareth Woods	16/03/2017 12:54
Simultaneous Equations	draft	Gareth Woods	04/07/2018 11:13
Gareth's copy of Gareth's copy of Gareth's copy of Denis's copy of Simultaneous equations (2)	draft	Gareth Woods	16/03/2017 12:54
Ian's copy of Simultaneous linear equations (variables)	draft	Ian Loasby	21/07/2017 13:14
Ioannis's copy of Lois's copy of Simultaneous linear equations (variables)	Needs to be tested	Ioannis Lignos	28/10/2018 19:30
Sistema de Ecuaciones (2x2) (2)	draft	Patricio Ramirez	14/01/2018 05:55
Sistema de Ecuaciones no Lineal (3)	draft	Patricio Ramirez	14/01/2018 06:05
Sistema de Ecuaciones no Lineal (4)	draft	Patricio Ramirez	14/01/2018 06:09
Sistema de Ecuaciones (2x2) (1)	draft	Patricio Ramirez	14/01/2018 05:54
Ecuación Radical reducible a Cuadrática	draft	Patricio Ramirez	02/12/2020 15:42
Ecuación de cuarto grado reducible a Cuadrática	draft	Patricio Ramirez	02/12/2020 15:42
Razones	draft	Patricio Ramirez	15/01/2018 06:00
proporcionalidad Inversa	draft	Patricio Ramirez	15/01/2018 06:54
proporcionalidad directa	draft	Patricio Ramirez	15/01/2018 05:51
Ecuación Radical reducible a Cuadrática .jk	draft	Jos Klenner	02/12/2020 15:42
Ecuación de cuarto grado reducible a Cuadrática.jk	draft	Jos Klenner	02/12/2020 15:42
Sistema de Ecuaciones no Lineal (4).jk	draft	Jos Klenner	15/01/2018 15:11
Sistema de Ecuaciones (2x2) (1).jk	draft	Jos Klenner	15/01/2018 15:12
Sistema de Ecuaciones no Lineal (3).jk	draft	Jos Klenner	15/01/2018 15:14
Sistema de Ecuaciones (2x2) (2).jk	draft	Jos Klenner	15/01/2018 15:16
Diagnostic Test - Simultaneous Equations	draft	Gareth Woods	04/07/2018 15:26
Simon's copy of Simultaneous linear equations (variables)	draft	Simon Thomas	21/03/2019 15:26
Third Form 2018 Question 15 (Essay)	Ready to use	sean hunte	08/05/2019 02:44
linear equations in 2 variables	draft	Thomas Waters	11/09/2019 21:43
Linear equations in 2 variables	draft	Thomas Waters	11/09/2019 22:26

There are 26 other versions that do you not have access to.

Question statement

Solve the following pair of simultaneous equations. You should write your answer as a simplified fraction in the form a/b, e.g. 3/4 or 12/5.

Give any introductory information the student needs.

			Name	Type	Generated Value

a4	integer	9
b4	integer	7
c4	integer	9
a5	integer	7
b5	integer	2
c5	integer	9

			Name	Type	Generated Value

a	integer	2
c	integer	2
b	integer	3
a1	integer	1
b1	integer	7
c1	integer	7
a3	integer	8
b3	integer	7
c3	integer	4
c2	integer	5
b2	integer	-6
a2	integer	6

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9 except[a,a1,a2,a3])

JME function reference

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`

← Depends on:

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

$\begin{eqnarray*} \simplify{{a}x+{b}y}&=&\var{c}\\\\\simplify{{a1}x+{b1}y}&=&\var{c1}\end{eqnarray*}$

$x=$ Gap 0.

$y=$ Gap 1.

Advice

Multiply the first equation by $\var{b1}$ and the second equation by $\var{b}$ so they both have the same $y$ coefficient:

$\begin{align} \simplify{{a*b1}x+{b*b1}y} &= \var{c*b1} \\ \simplify{{a1*b}x+{b1*b}y} &= \var{c1*b} \end{align}$

Next, subtract the second equation from the first to get

$\simplify[std]{{a*b1-a1*b}x} = \var{c*b1-c1*b}$

So $x = \simplify[std]{{(c*b1-c1*b)/(a*b1-a1*b)}}$ .

Substitute this value of $x$ into the first equation and rearrange to obtain $y$ :

$\begin{align} \simplify[std]{{a}*{(c*b1-c1*b)/(a*b1-a1*b)} + {b}y} &= \var{c} \\ \simplify[std]{{b}y} &= \simplify[std]{{c}-{a*(c*b1-c1*b)/(a*b1-a1*b)}} \\ y &= \simplify[std]{{(c-a*(c*b1-c1*b)/(a*b1-a1*b))/b}} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Simultaneous Equations by Gareth Woods in Gareth's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Gareth Woods 8 years ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Simultaneous Equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Gareth Woods 8 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`