Solving simultaneous equations. (Video)

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steve kilgallon

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steve kilgallon 8 years, 6 months ago

Created this as a copy of Solving equations. (Video).

Name	Status	Author	Last Modified
Solving equations. (Video)	Ready to use	Bill Foster	01/06/2016 09:47
Perdita's copy of Solving equations. (Video)	Ready to use	Perdita Harper	01/06/2016 09:47
Solve simulatenous equations. (Video)	Ready to use	Jinhua Mathias	28/08/2024 12:15
José's copy of Solve simulatenous equations. (Video)	Ready to use	Jos Klenner	02/12/2020 15:42
David's copy of Solving equations. (Video)	Ready to use	David Rickard	01/06/2016 09:47
joshua's copy of Solve simulatenous equations. (Video)	Ready to use	joshua boddy	01/06/2016 09:47
Lucy's copy of Solve simulatenous equations. (Video)	draft	Lucy Hadfield	03/08/2016 11:25
Solving simultaneous equations. (Video)	draft	steve kilgallon	05/09/2016 11:51
Ian's copy of Solving equations. (Video)	draft	Ian Loasby	21/07/2017 13:12
Simon's copy of Solving equations	draft	Simon Thomas	21/03/2019 15:27

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Question statement

Solve the following simultaneous equations for $x$ and $y$ . Input your answers as fractions or integers, not as decimals.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
c	integer	9
b	integer	-9
that	number	3
this	number	1
fromorto	string	to
s1	integer	1
s6	integer	1
a1	integer	3
aort	string	add the equation
a2	number	7
b1	integer	3
b2	integer	3
sc	integer	1
sb	integer	-1
sa	integer	1
sc1	integer	-1
c1	integer	-4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
sa*random(2..9)

JME function reference

Description

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

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Generated value: `integer`

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This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
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1. Step Information only

Gap-fill

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

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

$x=\phantom{{}}$ Gap 0., $y=\phantom{{}}$ Gap 1.

Input your answers as fractions or integers, not as decimals.

Click Show steps for a video that describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Advice

$\begin{eqnarray} \simplify[std]{{a}x+{b}y}&=&\var{c}&\mbox{ ........(1)}\\ \simplify[std]{{a1}x+{b1}y}&=&\var{c1}&\mbox{ ........(2)} \end{eqnarray}$
To get a solution for

$x$ multiply equation (1) by {this} and equation (2) by {that}

This gives:

$\begin{eqnarray} \simplify[std]{{a*this}x+{b*this}y}&=&\var{this*c}&\mbox{ ........(3)}\\ \simplify[std]{{a1*that}x+{b1*that}y}&=&\var{that*c1}&\mbox{ ........(4)} \end{eqnarray}$
Now {aort} (4) {fromorto} equation (3) to get

$\simplify[std]{({a*this}+{s6*a1*that})x={this*c}+{s6*that*c1}}$
And so we get the solution for

$x$ :

$x = \simplify{{c*b1-b*c1}/{b1*a-a1*b}}$
Substituting this value into any of the equations (1) and (2) gives:

$y = \simplify{{c*a1-a*c1}/{b*a1-a*b1}}$
You can check that these solutions are correct by seeing if they satisfy both equations (1) and (2) by substituting these values into the equations.

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This question is used in the following exams:

simultaneous equations by steve kilgallon in Algebra 1.
BY138 tutorial 3b (simultaneous equations) by steve kilgallon in BY138.
simultaneous equations by steve kilgallon in Algebra 1.

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Taxonomy: mathcentre

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steve kilgallon 8 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Solving simultaneous equations. (Video)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

steve kilgallon 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`