Algebra VIII: solving simultaneous equations (equate & substitute)

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Created this as a copy of Algebra VIII: solving simultaneous equations (equate & substitute).

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

Find the point of intersection of the following pair of straight lines by working through parts a) to d)

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	10
b	integer	-9
ans1	integer	51
ans2	integer	-29
ans3	integer	72
yCoef	integer	-8
n1	integer	6
n2	integer	1
n3	integer	-2
n4	integer	1

Automatically regenerate variables?

Name

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Value

xxxxxxxxxx
 
random(-10..10 except 0)

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Description

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Generated value: `integer`

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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

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.

By equating equation (1) and equation (2), we find that:

Unnamed gap $\simplify{x = {ans2} - {n4}*{ans1}/{n2}}$

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:

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

$\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) - {ans2} = 0}$

$\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} - {ans2} = 0}$

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

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

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

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Part	Test	Passed?
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This question is used in the following exam:

Test by Venkata Lakshmipathi Raju Chinthalapati in Venkata Lakshmipathi Raju's workspace.

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Algebra VIII: solving simultaneous equations (equate & substitute)

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Taxonomy: mathcentre

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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`

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Algebra VIII: solving simultaneous equations (equate & substitute)

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`