Systems of linear equations in 2 variables

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Vicky Hall

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Vicky Hall 8 years, 9 months ago

Created this as a copy of Simultaneous linear equations (variables).

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

Consider the following system of equations:

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	9
c	integer	2
b	integer	-6
a1	integer	7
b1	integer	9
c1	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)

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`

This variable doesn't seem to be used anywhere.

Parts

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.

Solve to find the values of $x$ and $y$ .

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

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

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Vicky Hall 8 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Systems of linear equations in 2 variables

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Vicky Hall 8 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`