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Achievement objective M8-8

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • form and use systems of simultaneous equations, including three linear equations and three variables, and interpret the solutions in context.


  • Translates contextual problems into systems of linear equations.
  • Solves problems that can be modelled by systems of three linear equations with up to three unknowns.
  • Chooses appropriate methods and uses them to solve simultaneous equations.
  • Understands the process of solving systems of equations algebraically.
  • Manipulates equations.
  • Interprets solution(s) of a linear system in context.
  • Identifies solutions that may be unique, infinite or non-existent.
  • Explains the nature of solution(s) including consistency and uniqueness and interprets this in context, including 3D.
  • Makes links to graphs M7-2 and manipulating expressions M7-6.
  • See key mathematical ideas on NZmaths.


M8-8 links from M7-8.

Possible context elaborations

  • Given total prices for three selected goods over three shopping sessions, calculate prices for individual goods.
  • Given a table of vitamin content in three types of energy drink and the total vitamins required, find how many cans of each kind of drink would fulfil the vitamin requirement.
  • Given a system of three equations, with parameters for coefficients, find values of parameters to satisfy particular solution situations, for example, a unique solution.
  • Given a contextual problem and a variety of systems of equations, select the equations that match the problem.
  • Given a variety of systems of three equations, select those that involve parallel planes.

Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

Learn more:

The following achievement standard(s) could assess learning outcomes from this AO:

  • AS91587 Mathematics and statistics 3.15 Apply systems of simultaneous equations in solving problems; Internal, 3 credits.

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013