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.
How Many Solutions?
The following videos explore in more depth how many solutions simultaneous equations can actually have.
Systems of Simultaneous Equations Practice Questions
The video below covers a large number of examples of simultaneous equations problems, and the approach to solve it.
Want to learn more? Check out more of our VCE Mathematics resources here!