9-1 Solving 3 by 3 Systems Day 1.

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Presentation transcript:

9-1 Solving 3 by 3 Systems Day 1

Umm… did she say 3 by 3?? Just like the 2 by 2 systems, we will solve the 3 by 3 systems. How many methods did we choose from to solve the 2 by 2’s? Substitution 2. Addition/Subtraction

Conveniently, there are 3 methods we can use here Today will be the first two Substitution Addition/Subtraction Follow all directions, but unless specified you can use any method.

Guess which method would be best here: 1. Yes – substitution is best for this type of problem. Specifically it is called “back substitution” because you substitute backwards from simplest to most complicated. However, substitution can be messy if there are multiple variables in each equation. Instead, you should probably

Try Elimination 2. WAIT! There is a method to these problems. Lets think talk it through logically before we actually do this problem.

Method Careless mistakes will crush you here. Be very careful and keep this in mind. Pick one variable to eliminate and do it twice (you will end up with two equations with two matching unknowns) 2. Solve for one variable; back substitute to find the other variables. 3. Label the equations carefully so you can keep track.

OK – try it now. 2. 3.

One last thing: What will you see with a no solution or what we used to call “infinite number of solutions?” If you get something false (0 = 4) then there is no solution.

What if you get a True Statement? In this situation, the planes intersect at a line.