Solving Simultaneous Equations

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Question statement

Solving Simultaneous Equations using Matrices

Simultaneous equations consist of two equations with two unknown values and both equations must be solved at the same time. This can be done using matrices.

Consider the following set of simultaneous equations:

$\begin{align} \simplify{{mA[0][0]}x + {mA[0][1]}y} &= \var{mC[0][0]} \\ \simplify{{mA[1][0]}x + {mA[1][1]}y} &= \var{mC[1][0]} \end{align}$

We can solve these equations using the following steps:

(Input all numbers as fractions or integers and not as decimals.)

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	9
y	integer	6
mA	matrix	matrix([-2,5],[7,9])
mC	matrix	matrix([12],[117])
mAI	matrix	Matrix of size 2×2
det_mA	number	-53
sx	string	x
sy	string	y

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)*random(1,1,1,-1)

JME function reference

Description

value for x

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

Part a) Gap-fill
1. Gap Gap 0. Matrix entry
  Add
2. Gap Gap 1. Mathematical expression
  Add
3. Gap Gap 2. Mathematical expression
  Add
4. Gap Gap 3. Matrix entry
  Add
Part b) Matrix entry
Part c) Matrix entry
Part d) 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.

First, rewrite the equations in matrix form of $Ab = C$ , where the matrix $A$ will contain the coefficients of the equation, $b$ will contain the unknown values and $C$ will contain the constants.

$\mathbf{A} =$ Gap 0.

$\mathbf{b} =$

Gap 1.

Gap 2.

$\mathbf{C} =$ Gap 3.

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Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
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Number entry
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Gap-fill
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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Mark Patterson 4 years, 6 months ago

Mark Patterson 4 years, 6 months ago

Mark Patterson 4 years, 6 months ago

Solving Simultaneous Equations using Matrices

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Solving Simultaneous Equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mark Patterson 4 years, 6 months ago

Mark Patterson 4 years, 6 months ago

Mark Patterson 4 years, 6 months ago

Solving Simultaneous Equations using Matrices

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`