Systems of Simultaneous Equations

What are simultaneous equations?

In this post, we solve practical problems involving a pair of simultaneous linear and/or quadratic functions algebraically and graphically. This is part of the VCE Maths Methods course under the topic Algebra and sub-part Solving Equations, specifically focusing on solving systems of simultaneous equations. We also understand that solving $f(x) = k$ corresponds to finding the values of $x$ for which the graph $y = f(x)$ cuts the line $y = k$ .

Simultaneous equations are two or more lines of equations that share a common variable. In simultaneous equations, there are as many equations as there are variables, and this allows us to be able to solve them simultaneously.

Introduction to simultaneous equations

The following two videos introduce simultaneous equations. The first video covers the theory of understanding that simultaneous equations can have more than one solution, and the second video covers a visual method of solving.