Solving two linear equations

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Frank Doheny

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7 years, 4 months ago

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Frank Doheny 7 years, 4 months ago

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Frank Doheny 8 years, 4 months ago

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Frank Doheny 8 years, 6 months ago

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Name	Status	Author	Last Modified
Solving two linear equations	Ready to use	Frank Doheny	24/11/2017 07:39
Ann's copy of Solving two linear equations	draft	Ann Smith	21/06/2018 11:29

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Question statement

Solve the following system of simultaneous equations:

$\var{a}x+\var{b}y=\var{r1}$

and

$\var{c}x+\var{d}y=\var{r2}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
b	integer	3
c	integer	4
d	integer	12
r1	integer	28
r2	integer	47

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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:

Statement
Advice
Variable testing condition
"Unnamed part" → "Gap 0." - Minimum accepted value
"Unnamed part" → "Gap 0." - Maximum accepted value
"Unnamed part" → "Gap 1." - Minimum accepted value
"Unnamed part" → "Gap 1." - Maximum accepted value

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.

Input the value for $x$ as an exact fraction.

$x =$ Gap 0.

Input the value for $y$ as an exact fraction.

$y =$ Gap 1.

Advice

equation (i) $\var{a}x+\var{b}y=\var{r1}$

equation (ii) $\var{c}x+\var{d}y=\var{r2}$

If we decide to eliminate the $x$ variables we need to have the same number of $x$ in both equations

$\var{c}$ *equation (i) $\simplify{{c}*{a}}x+\simplify{{c}*{b}}y=\simplify{{c}*{r1}}$

$\var{a}$ *equation (ii) $\simplify{{c}*{a}}x+\simplify{{d}*{a}}y=\simplify{{a}*{r2}}$

Subtracting gives:

$\simplify{{c}*{b}-{d}*{a}}y=\simplify{{c}*{r1}-{a}*{r2}}$

$y=\simplify{({c}*{r1}-{a}*{r2})/({c}*{b}-{d}*{a})}$

Substituting this solution for $y$ into equation (i) gives

$\var{a}x+\var{b}*(\simplify{({c}*{r1}-{a}*{r2})/({c}*{b}-{d}*{a})})=\var{r1}$

$\var{a}x=\var{r1}-\var{b}*(\simplify{({c}*{r1}-{a}*{r2})/({c}*{b}-{d}*{a})})$

$\var{a}x=\simplify{{r1}-{b}*({c}*{r1}-{a}*{r2})/({c}*{b}-{d}*{a})}$

$x=\simplify{({r1}-{b}*({c}*{r1}-{a}*{r2})/({c}*{b}-{d}*{a}))/{a}}$

Give a worked solution to the whole question.

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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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Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Solving two linear equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`