Systems of Linear Equations (DP IB Analysis & Approaches (AA): HL): Revision Note

A linear equation is an equation of the first order (degree 1)

• e.g.

• A linear equation cannot have terms like , , , etc

A system of linear equations means a set of linear simultaneous equations

If there are variables (letters)

• then you will need at least equations in order to solve it

  • For your exam, will be 2 or 3

A 2×2 system of linear equations can be written as

A 3×3 system of linear equations can be written as

Systems of linear equations can represent lines in 2D or planes in 3D

For a 2×2 system

• Each equation will represent a straight line in 2D

• The solution (if it exists and is unique) will correspond to the coordinates of the point where the two lines intersect

For a 3×3 system

• Each equation will represent a plane in 3D

• The solution (if it exists and is unique) will correspond to the coordinates of the point where the three planes intersect

For questions where not all equations are given, you may need to read through a context and

• introduce your own letters, e.g.

• find a missing equation from words

Your GDC has a function within the algebra menu to solve a system of linear equations

• You will need to choose the number of equations

  • For two equations, the variables will be and

  • For three equations, the variables will be , and

Equations must be rearranged into the correct form first

• e.g.

  • 

  • 

Your GDC will then display the values of and (or , and )

• These are the solutions