Solve a pair of simultaneous equations

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Solve a pair of simultaneous equations	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Solve a pair of simultaneous equations	draft	Luis Hernandez	30/11/2018 17:39
John's copy of Solve a pair of simultaneous equations	draft	John Wick	10/07/2019 15:21
Roz's copy of Solve a pair of simultaneous equations	draft	Roz Wyatt-Millington	27/09/2019 09:30
Intersezione di due rette nel piano cartesiano (soluzione analitica)	Ready to use	Irene Paniccia	30/03/2023 15:29

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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	-2
c	integer	-8
b	integer	8
that	number	4
this	number	1
sc1	integer	1
s1	integer	-1
s6	integer	-1
a1	integer	7
aort	string	take away the equation
a2	number	2
b1	integer	2
b2	integer	2
sc	integer	-1
sb	integer	1
sa	integer	-1
fromorto	string	from
c1	integer	8

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.

Can an exam override the value of this variable?

Generated value: `integer`

-2

← Depends on:

→ Used by:

Advice
"Unnamed part" - prompt
"Unnamed part" → "Gap 0." - Correct answer
"Unnamed part" → "Gap 1." - Correct answer

Parts

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

See "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.

Give a worked solution to the whole question.

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Part	Test	Passed?
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Mathematical expression
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Bill Foster 6 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Solve a pair of simultaneous equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`