Simultaneous equations by substitution 2

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9 years, 6 months ago

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joshua boddy 9 years, 6 months ago

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joshua boddy 9 years, 7 months ago

Created this as a copy of Simultaneous equations.

Name	Status	Author	Last Modified
Simultaneous equations by substitution 2	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 2	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 1	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 1 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 3 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 1 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by substitution 2 with parts	Ready to use	joshua boddy	04/02/2021 23:31
Simultaneous equations by elimination 2 with parts	Ready to use	joshua boddy	01/06/2016 09:47
Simultaneous equations by elimination 3	Ready to use	joshua boddy	01/06/2016 09:47
Numerical Skills - Simultaneous equations by elimination 1	Ready to use	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Simultaneous equations by elimination 2	Ready to use	Jinhua Mathias	28/08/2024 12:15
Numerical Skills - Simultaneous equations by elimination 1 summative	Ready to use	Jinhua Mathias	28/08/2024 12:15
Algebra VIII: solving simultaneous equations (by elimination)	Ready to use	Luke Park	15/09/2016 13:25
Algebra VIII: solving simultaneous equations (rearrange & substitute)	Ready to use	Jinhua Mathias	27/08/2024 16:37
Algebra VIII: solving simultaneous equations (equate & substitute)	Ready to use	Luke Park	08/08/2016 16:16
Algebra VIII: solving Linear equations (rearrange & substitute)	Ready to use	Nasir Firoz Khan	12/08/2016 16:12
Simultaneous equations by elimination	draft	Francis Duah	14/09/2016 12:27
Francis 's copy of Algebra VIII: solving simultaneous equations (equate & substitute)	draft	Francis Duah	14/09/2016 13:04
Hania's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Hania Jasiczak	05/10/2016 14:42
Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Seibu Mary Jacob	18/01/2017 13:42
Jerome's copy of Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Jerome Leary	20/01/2017 22:20
Denis's copy of Seibu Mary's copy of Algebra VIII: solving simultaneous equations (by elimination)	draft	Denis Flynn	11/02/2021 12:04
Algebra VIII: solving simultaneous equations (by elimination)	Ready to use	heike hoffmann	14/11/2018 22:29
Algebra VIII: solving simultaneous equations (equate & substitute)	Ready to use	heike hoffmann	14/11/2018 22:31
Simultaneous equations by elimination 2	draft	Xiaodan Leng	11/07/2019 05:39
Viet's copy of Simultaneous equations by elimination 2	draft	Viet Hoang	13/08/2019 22:23

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-3
b	integer	-2
ans1	integer	19
ans2	integer	28
ans3	integer	-162
yCoef	integer	81
n1	integer	-1
n2	integer	-8
n3	integer	-10
n4	integer	1

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random(-10..10 except 0)

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Generated value: `integer`

-3

→ Used by:

ans1
ans2
b

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Parts

Gap-fill

Gap-fill

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Solve the pair of equations

$\begin{eqnarray} \simplify{{n1}*x + {n2}*y} & = & \var{ans1} &&&&&&&(1)\\ \simplify{{n3}*x + {n4}*y} & = & \var{ans2}&&&&&&&(2)\end{eqnarray}$

We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

We start by rearranging equation (1) like so:

$y =$ Gap 0., (3)

Substitute equation (3) into equation (2) to give:

Gap 1. $\simplify{x + {n4}*{ans1}/{n2} = {ans2}}$

Solve this linear equation to give $x =$ Gap 2.,

Substitute the value of x back into equation (1) to find

$y =$ Gap 3.

Advice

We are going to solve for $x$ first. To do this, we need to eliminate $y$ from the equations.

We start by rearranging equation (1) like so:

$\simplify{y = 1/{n2}*({ans1}-{n1}*x)}$

$\simplify{{n3}*x + {n4}/{n2}({ans1}-{n1}*x) = {ans2}}$

$\simplify{({n3}-{n1}*{n4}/{n2})*x + {n4}*{ans1}/{n2} = {ans2}}$

$\simplify{x=({n4}*{ans1}-{n2}*{ans2})/({n1}*{n4}-{n3}*{n2})}$

Substitute the value of x back into equation (1) to find

$\simplify{y=({ans1}*{n3}-{n1}*{ans2})/({n2}*{n3}-{n1}*{n4})}$

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joshua boddy 9 years, 6 months ago

joshua boddy 9 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Simultaneous equations by substitution 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

joshua boddy 9 years, 6 months ago

joshua boddy 9 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`