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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.

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

Last updated September 14, 2018