8.2. Systems of Three Equations and Three Unknowns http://www.ck12.org
8.2 Systems of Three Equations and Three Un-
knowns
Here you will extend your knolwedge of systems of equations to three equations and three unknowns.
Later, you will learn about matrices and how to row reduce which will allow you to solve systems of equations in
a new way. In order to set you up so that using matrices is logical and helpful, it is important to first solve a few
systems of three equations using a very specific type of variable elimination.
When solving systems, what are you allowed to do to each equation?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61412http://www.youtube.com/watch?v=3RbVSvvRyeI James Sousa: Ex 1: System of Three Equations with Three
Unknowns Using Elimination
Guidance
A system of three equations with three unknowns represents three planes in three dimensional space. When solving
the system, you are figuring out how the planes intersect. It is possible that the three planes could intersect in a
point:
It is also possible for two or more planes to be parallel or each pair of planes to intersect in a line. In either of these
cases the three planes do not intersect at a single point and the system is said to have no solution. If the three planes
intersect at a line or a plane, there are an infinite number of solutions.