Types of solutions
for systems of planes (3 variable equations)
What is a solution of system of equations with 3 variables?
Why are we going to use 3 planes?
If you want to solve an equation with 2 variables, you need 2 equations.
You can's solve x + y =1 , right? That's because you 1 equation with 2 variables
Similarly, if you have an equation with 3 variables, (3 planes), you're going to need 3 equations to solve it
Two important terms
Means that there is at least 1 intersection (solutions)
Means that there are no intersections(solutions)
Ok, so how do we find that point of intersection?
Video Tutorial on using Elimination
Example of how to solve a system of three variable equations using elimination.
Although you can indeed solve 3 variable systems using elimination and substitution as shown on this page, you may have noticed that this method is quite tedious. The most efficient method is to use matrices or, of course, you can use this online system of equations solver. (all of our pictures on this topic)