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terms in the expression 3x1 − x2 . Coupling more than one linear equation in n variables results
in a system of linear equations in n variables. When solving these systems, it becomes
increasingly important to keep track of what operations are performed to which equations and to
develop a strategy based on the kind of manipulations we’ve already employed. To this end, we
ﬁrst remind ourselves of the maneuvers which can be applied to a system of linear equations that
result in an equivalent system.9 4 In the case of systems of linear equations, regardless of the number of equations or variables, consistent independent systems have exactly one solution. The reader is encouraged to think about why this is the case for linear
equations in two variables. Hint: think geometrically.
The adjectives ‘dependent’ and ‘independent’ apply only to consistent systems - they describe the type of solutions.
If we think if each variable being an unknown quantity, then ostensibly, to recover two unknown quantities,
we need two...
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