Topics:
• Solving systems of linear equations: what does “linear” mean? Classification according to the number of solutions.
The pictures I used in class came from these two sites:
Systems of linear equations at Math is Fun
Solving linear systems in three variables
The basic classification is this:
Inconsistent system: has no solutions
Consistent, independent system: has exactly one solution
Consistent, dependent system: has infinitely many solutions
• Solving nonlinear systems using substitution and using elimination
here is the handout outline notes with the two examples we worked on in class:
You can use them to rework those examples if you want.
Pay attention to choosing the method you will use when solving nonlinear systems. Also remember to be very careful to separate out the multiple solutions as you go!
• Trigonometry topic: special right triangles
We only discussed the isosceles right triangle (and this is the name you should use, rather than any name that refers to the degree measures of its angles, since we will be using another measure (radians) rather than degrees!
The two important right triangles are:
• The isosceles right triangle,
• The half of an equilateral triangle (to be discussed next time) – which I will call the half-equilateral triangle for short.
These are commonly called by other names which refer specifically to the degree measure of their angles, but it is much better to call them by these names for two reasons (at least):
• Later we will use the radian measure of the angles, so we do not want to tie ourselves too much to degree measure
• The names given above remind us of what these triangles really are, so that we can recreate them if we forget the relationships of their sides, for example.
Homework:
• Review solving nonlinear systems. It is a really good idea to graph your system on Desmos (when you have access to it) so you can check that you have the right number of solutions, since that can be rather challenging to predict otherwise!
• Do the WeBWorK on this topic – it is not due until Sunday evening, but don’t put it off! Do at least some of it now.
• Review the isosceles right triangles and how we found the length of the hypotenuse using the Pythagorean Theorem. If you do this a few times, you will end up memorizing the triangle! You must learn it by heart as we will use it (and the other special right triangle) a lot in Trigonometry.
• Start working on the WeBWorK on that topic also. (You may not be able to do it all yet.)
• From the Algebra textbook, do the assigned problems from Section 9.4
• Read this web page on the isosceles right triangle and work the Review problems at the end of it.
• Please note that we will be working from the Trigonometry textbook for most of the remainder of the semester.
Remember that you can use the Piazza discussion board to ask questions if you get stuck on any of the WeBWorK or the other homework problems. Don’t forget to include the problem itself in your question, as that will make it easier for you to get a quick response!
