Unit+2

__**Unit 2: Systems of Equations**__ = = = ‍Journal Assignments: All due dates are listed on your teacher's site (when the journal entry should be finished). =

‍__**2.1:**__
Using a sheet of graph paper, graph each pair of equations on the same coordinate system. (There should be 2 lines on each graph.) __**You may use the document link below to help organize your thinking process and for the coordinate planes.**__

[|2.1 journal response.doc]

Answer the following questions __**on your graph paper or on the document you printed**__ and put your work in your classroom binder.
 * Identify how many intersections are shown on each graph.
 * Now look at the 2 equations that made the first graph. What is the relationship of their slopes?
 * Looking at the 2 equations that made the second graph, what is the relationship between their slopes?
 * Looking at the 2 equations that made the third graph, what is the relationship between their slopes?

__**On your wikispace**__, describe the relationship between different pairs of lines and their slopes as it relates to the number of intersections (solutions) that the system of equations will have. Be sure to discuss all 3 graphs and how they are similar or different.

**Answer:**

__2.2:__
Describe the 3 different methods for solving (finding a solution) to a system of equations. Why/When would you choose one method over the another? What are you looking for in each system to determine the best method? Discuss any tricks or special techniques to remember when solving each of the methods.

In each system you are suppose to look for the variables in each system to determine the best method.
 * Answer: **
 * The three different methods for solving to a system of equations are: **
 * Solve a system of linear equations in two variables by graphing.
 * Solve a system of linear equations in two variables by the substitution method.
 * Solve a system of linear equations in two variables by the elimination method.

Look at the graph below. Both functions represent two different bank accounts.
**The blue linear function represents a bank account where a person deposited $1000. This person then deposits an additional 100 dollars at the end of each year.**

**The red linear function represents a bank account where a person deposited $1050. This person then deposits an additional 75 dollars at the end of each year.**

Compare and contrast the two bank accounts in your online journal by answering the following questions:


 * Write a function that represents the red linear function.
 * What is the y-intercept of each function? Explain in the context of the situation.
 * What is the slope of each function? Explain in the context of the situation.
 * Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
 * Which account would you choose when opening to save up for your college in a few years and why?
 * Would you choose that same account to start your child's college fund (if you had a child) and why?


 * Answer: **
 * ** The function that represents the red linear function is : y = 1000x+3 **
 * ** The y-intercept of each function is 100 and 75 and it represents the additional deposit at the end of each year. **
 * ** The slope of each function is1000 and 1050 which represents the bank accout where a person put his money. **
 * ** The blue one is better because it is the higher and longer. At first the red appeared to be better, but it is not always true. Along the way the blue account become better. **
 * ** I woul choose the blue accout because when opening to save up for college because it is the better one. **