Jessica's copy of Simultaneous linear equations (variables)

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Jessica Ryan

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Christian Lawson-Perfect

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8 years, 9 months ago

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Christian Lawson-Perfect 8 years, 9 months ago

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Jessica Ryan 9 years, 7 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
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There are 26 other versions that do you not have access to.

Question statement

Solve:

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
c	integer	8
b	integer	-7
a1	integer	5
b1	integer	2
c1	integer	3

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`

→ Used by:

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Mathematical expression
  Add

Gap-fill

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

$x=$ Gap 0.

$y=$ Gap 1.

input your answers as fractions and not as decimals.

Advice

Elimination method:

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 $y$ :

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

Substitution method:

Rearrnge both equations to make $y$ the subject:

$y=\simplify{({c}-{a}x)/{b}}$

$y=\simplify{({c1}-{a1}x)/{b1}}$

Then substitute the first equation into the second:

$\simplify{({c}-{a}x)/{b}}=\simplify{({c1}-{a1}x)/{b1}}$

Now we have an equation in only one variable, which can be rearranged and solved to find $x$:

\[\simplify{{c}-{a}x}=\simplify{{b}(({c1}-{a1}x)/{b1})}\]

\[\Rightarrow \var{a}x=\simplify{-{b}(({c1}-{a1}x)/{b1})+{c}}\]

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

We can now substitute this value of $x$ into the first equation and rearrange to obtain $y$ :

Give a worked solution to the whole question.

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This question is used in the following exam:

DT203/299T CA by Blathnaid Sheridan in Blathnaid's workspace.

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Jessica's copy of Simultaneous linear equations (variables)

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Jessica Ryan 9 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Error

Jessica's copy of Simultaneous linear equations (variables)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Jessica Ryan 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`