# SACE Stage 2 General Mathematics – Modelling with Linear Relationship

1.1 Simultaneous Linear Equations

1.2 Linear Programming

Students review the concepts of continuous linear functions studied in Linear and exponential functions and their graphs in Stage 1 General Mathematics and extend their understanding through solving problems involving simultaneous linear equations. Linear programming is introduced as a major application of linear functions. The solution to problems involving the interaction of two variables is investigated in depth. At first, students solve problems set in realistic contexts with which they are familiar. They are encouraged to solve these problems by trial and error before being presented with the linear programming algorithm so that they can appreciate the dynamic nature of the problems.

Problems are posed in everyday contexts. Examples of situations where these techniques are used are discussed with or researched by students.

Students investigate the effects on the optimal solution of changing the initial parameters in some problems. For instance, what effect will change the objective function or the constraints have on cost, profit, or wastage? In situations with multiple optimal solutions, students discuss the merits of the different choices beyond the value of the objective function. Students explore situations involving discrete and continuous variables and understand how to appropriately deal with an optimal solution that is not achievable in a context where only discrete values of the variables are acceptable.

Students use electronic technology to support the efficient solution of pairs of simultaneous linear equations and the investigation of linear programming scenarios.

*Source – Subject Outline, South Australian Certificate of Education 2023*

SACE Stage 2 General Mathematics Courses

SACE Stage 2 General Mathematics Syllabus

## Course Content

### Simultaneous Equations

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