Linear Simultaneous Equations
Friday, September 6, 2019
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Solving linear simultaneous equations is rather satisfying. In this postal service I advise approximately techniques too resources for pedagogy this topic.
Equality too Lincoln
When I saw the cinema Lincoln I was struck yesteryear Abraham Lincoln’s reference to Euclid’s First Axiom ‘Things which are equal to the same matter are also equal to ane another’. Influenza A virus subtype H5N1 well-made betoken inward a give-and-take nearly racial equality, but also an interesting claw into a method for solving simultaneous equations such as
Elimination too 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils abide by it really slow to recall the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inward the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inward each equation is positive (‘same sign’), we subtract one equation from the other.
However, I noticed that when solving simultaneous equations such every minute -3x + 5y = 41; 2x + 5y = 56, approximately pupils saw that the -3x too the 2x were different signs too incorrectly decided that this meant they should add the 2 equations. So it’s worth clarifying which signs nosotros are referring to inward the ‘Same Sign Subtract’/’Different Sign Add’ approach.
Graphical Solutions
It’s then of import for pupils sympathise that whenever they solve linear simultaneous equations, they are inward fact finding the betoken of intersection of 2 direct lines. It’s essential to position a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) too perish them thinking nearly why at that spot are no solutions. I similar to present them this cute picture too.
Wordy Equations
This is ane of my favourite simultaneous equation questions: “A zoo has several ostriches too several giraffes. In full they convey xxx eyes too 44 legs. How many ostriches too how many giraffes are inward the zoo?”. Make certain you lot discourage pupils from using the missive of the alphabet O for ostrich, because it looks similar a zero.
Resources
There's lots of resources online – here’s a few I’ve picked out:
Equality too LincolnWhen I saw the cinema Lincoln I was struck yesteryear Abraham Lincoln’s reference to Euclid’s First Axiom ‘Things which are equal to the same matter are also equal to ane another’. Influenza A virus subtype H5N1 well-made betoken inward a give-and-take nearly racial equality, but also an interesting claw into a method for solving simultaneous equations such as
y = 4x + 6
y = 2x + 3
Both 4x + six too 2x + three are equal to y, thus logically nosotros convey 4x + six = 2x + three (this is essentially merely a exchange method). Why non present this this blog gives a adept explanation of Lincoln's point)Elimination too 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils abide by it really slow to recall the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inward the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inward each equation is positive (‘same sign’), we subtract one equation from the other.
However, I noticed that when solving simultaneous equations such every minute -3x + 5y = 41; 2x + 5y = 56, approximately pupils saw that the -3x too the 2x were different signs too incorrectly decided that this meant they should add the 2 equations. So it’s worth clarifying which signs nosotros are referring to inward the ‘Same Sign Subtract’/’Different Sign Add’ approach.
Graphical Solutions
It’s then of import for pupils sympathise that whenever they solve linear simultaneous equations, they are inward fact finding the betoken of intersection of 2 direct lines. It’s essential to position a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) too perish them thinking nearly why at that spot are no solutions. I similar to present them this cute picture too.Wordy Equations
This is ane of my favourite simultaneous equation questions: “A zoo has several ostriches too several giraffes. In full they convey xxx eyes too 44 legs. How many ostriches too how many giraffes are inward the zoo?”. Make certain you lot discourage pupils from using the missive of the alphabet O for ostrich, because it looks similar a zero.
Resources
There's lots of resources online – here’s a few I’ve picked out:
- Don Steward’s Median blog has a huge make of fantastic questions too activities.
- TeachitMaths has a swell ‘wordy question’ worksheet too clear slides on elimination too substitution.
- UEA has a worksheet on linear simultaneous equations amongst a overnice progression of questions.
- There is a useful worksheet on Solving Simultaneous Equations Graphically yesteryear Tristan Jones on TES.
- This Geogebra worksheet yesteryear themathsteacher.com is a adept practise inward solving simultaneous equations graphically amongst ICT.
- Peter Bland and JustMaths both render assay questions on this topic.
- MEI has a overnice extension activity.