# Systems of Equations

**The 1997-8 El Nino ...**

Warmest ocean surface areas in red

The El Nino occurs every few years due to an increase in the sea temperature to the west of South America. The El Nino causes extreme weather around the globe, including droughts in Australia and Asia.

Climatologists use very interesting mathematics to try to predict this event.

**Modelling** changes in the climate requires an
understanding of many types of **equations**,
including **simultaneous equations.**

In this chapter, we see how to solve simple sets of linear equations and go on to solve pairs of non-linear equations.

## In this Chapter

- 1. Simultaneous Linear Equations - a brief introduction to what "simultaneous equations" means
- 2. Graphs of Linear Functions - an overview on the equation of a straight line
- 3. Graphical Solution of Linear Systems - how to solve a system of linear equations using graphs
- 4. Algebraic Solutions of Linear Systems - using algebra to find solutions
- 5. Graphical Solution of non-linear Systems - this involves curves that intersect
- 6. Algebraic Solution of non-Linear Systems - using algebra to find intersection points

We begin with the definition of simultaneous linear equations »