Simultaneous Equations with Three Unknowns (Leaving Cert Mathematics): Flashcards

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Simultaneous Equations with Three Unknowns
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How many variables in a 3-equation linear system?

Three variables (xx, yy, zz)

What space do 3-variable equations exist in?

Three-dimensional (3D) space

What does each 3-variable equation represent geometrically?

A plane (not a line)

What does solving 3 equations in 3 unknowns mean?

Finding the point of intersection of all 3 planes

Most common method for 3 equations in 3 unknowns

Elimination method

Elimination method Step 1

Pick any 2 equations and eliminate a variable

Elimination method Step 2

Pick another pair and eliminate the SAME variable

Elimination method Step 3 result

Two equations of two unknown variables

Elimination method Step 4

Substitute solved variables into an original equation

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