VCE · Foundation Maths · Algebra & Patterns live from the app

Solving Linear Equations

The goal is to get the unknown variable alone by undoing operations in reverse order using balance principles. Whatever you do to one side must be done to the other to maintain equality. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

foundation maths · algebra & patterns · solving linear equationsdrag it · it is yours
the one idea

why this one carries the topic.

Every rule here is one steady relationship: change one thing by a step, the other moves by the same step, every time. Formula, sequence, equation, line — four ways of writing that relationship.

Solving linear equations requires performing inverse operations in reverse order on both sides to isolate the variable while maintaining the equality balance.

what examiners catch — Students commonly fail when they only apply operations to one side, or when they incorrectly handle negative coefficients by forgetting to flip signs when dividing by negatives.
what you leave with

three things, not forty.

what's underneath

nothing here is a standalone fact.

knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 2 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptsolving linear equationsSolving linear equations requires performing inverse operations in reverse order on both sides to isolate the variable while maintaining the equality balance.
sits under itsubstitution into formulasbecause solving is substitution run backwards
built on itlinear relationshipsbecause a gradient and intercept are read off an equation you can already rearrange
built on itsimultaneous equations and the break-even pointbecause a pair is still solved one equation at a time — rearranging comes first
the rest of algebra & patterns

5 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

patterns and linear relationshipsin the appgraphs and models of practical situationsin the applinear sequencesin the appusing formulasin the appsubstitution into formulasin the app
this is one of 865

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knowherevce foundation mathssolving linear equations