1. Systems of Equations and Inequalities Ryan Morris Josh Broughton

2. Solving Systems of Equations Elimination Substitution Graphical For a system of linear equations, the solutions can be: one solutions, no solution, or infinite solutions Gaussian Elimination uses back substitution for more than two variable equations

3. Elimination

4. Systems Using Matrices In a system with more than two variables you can get rid of variables to solve Reduced Row Echelon Every number above and below each leading entry is 0 Bottom row has all zeros Leading entry is 1 and for each successive row, the entry is to the right of the entry of the row above Meet above conditions using row arithmetic

5. Matrix Algebra http://www.youtube.com/watch?v=fxKMAWT 2kC4 http://www.youtube.com/watch?v=fxKMAWT 2kC4 Start at 2:50

6. Matrix Algebra A matrix is given a variable You can add, subtract, and even multiply these matrices, using variables to keep it simple You cannot add or subtract matrices if they have different dimensions When you multiply matrices you multiply rows of a by columns of b

7. Cramer's Rule

8. Cramer’s Rule Is a way of solving a set of linear equations by using the quotient of determinants The numerator determinate is determined by substituting the solution vector for the variable column in the matrix The denominator matrix is the coefficient matrix

9. Systems of Inequalities Deal with regions rather than a small set of numbers They can be solved by comparing the graphs of the functions and observing where they overlap and using test points to check the inequalities