Linear Simultaneous Equations

Solving linear simultaneous equations is rather satisfying. In this postal service I advise unopen to techniques as well as resources for pedagogy this topic.

Equality as well as 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 affair are also equal to 1 another’. Influenza A virus subtype H5N1 well-made indicate inwards a tidings nigh racial equality, but also an interesting claw into a method for solving simultaneous equations such as

y = 4x + 6

y = 2x + 3

Both 4x + vi as well as 2x + three are equal to y, hence logically nosotros convey 4x + vi = 2x + three (this is essentially simply a exchange method). Why non demo this this blog gives a proficient explanation of Lincoln's point)

Elimination as well as 'SSS'
When solving simultaneous equations yesteryear elimination, my pupils uncovering it real tardily to shout out back the ‘SSS’ dominion ie ‘Same Sign Subtract’. For example, inwards the equations 3x + 5y = 59; 2x + 5y = 56, this dominion says that because the 5y inwards each equation is positive (‘same sign’), we subtract one equation from the other.

However, I noticed that when solving simultaneous equations such every 2nd -3x + 5y = 41; 2x + 5y = 56, unopen to pupils saw that the -3x as well as the 2x were different signs as well as incorrectly decided that this meant they should add the 2 equations. So it’s worth clarifying which signs nosotros are referring to inwards the ‘Same Sign Subtract’/’Different Sign Add’ approach.

Graphical Solutions
It’s as well as then of import for pupils empathise that whenever they solve linear simultaneous equations, they are inwards fact finding the indicate of intersection of 2 conduct lines. It’s essential to put a query involving parallel lines (eg solve 3x + 4y = 10; 6x + 8y = 15) as well as decease them thinking nigh why at that spot are no solutions.  I similar to demo them this cute picture too.

Wordy Equations
This is 1 of my favourite simultaneous equation questions: “A zoo has several ostriches as well as several giraffes. In full they convey xxx eyes as well as 44 legs. How many ostriches as well as how many giraffes are inwards the zoo?”. Make certain yous 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 arrive at of fantastic questions as well as activities.
• TeachitMaths has a slap-up ‘wordy question’ worksheet as well as clear slides on elimination as well as 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 proficient practice inwards solving simultaneous equations graphically amongst ICT.
• Peter Bland and JustMaths both supply examination questions on this topic.
• MEI has a overnice extension activity.