Systems of Equations

As I was preparing one of my lectures on systems of linear equations in 2 variables for my math class, I was saddened to realize that we do not cover matrices. Oh the humanity! Matrices are my favorite way to solve systems of linear equations. Then I was thinking....how would I rate the different methods of solving systems of linear equations.
Example:
3x-2y=-4
5x+y=15

1. Matrices. Matrices can solve linear equations with many variables and they are so awesome cool. Eigenvalues and determinants - yea! Give me some dark chocolate and some matrices and I'm in heaven!
2. Elimination. I just love eliminating variables by multiplying through the equation by a factor or what's even better, when you notice a variable can be eliminated without multiplying through. You'd see something like this:
x+y=8
x-y=2
3. Graphing. Who doesn't love graphing? The point at which the lines intersect is the solution to the system of linear equations. You get to play with your graphing calculator (or do it by hand if you are a rebel) to find the answer. Sometimes it's hard to find the exact point especially if it is something like (42/13, 11/26) so you might have to use your spidey sense. The way the graphing calculator spins those lines kind of reminds me of spiderman. With great power comes great responsibility!
4. Substitution. Sometimes this method works really well such as:
2x+7=-12
x=3-2y
but most of the time you have to solve for one of the variables. Not that it is that difficult, but I don't want to spend time doing that - I just want to dive into solving the system.


10 points to anyone who solves all of the above equations. Although I don't know what you would do with 10 points :). I'm not taking anyone to the Cheesecake factory that's for sure.

68 points on quiddler today