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toc = **Chapter 8: Systems of Equations** = Preview: [|Chapter 8 Preview 1011.pdf]

**Wiki Summaries**
//**Due the school day after we cover the lesson in class **// 8-1: Derik K. and Brianna P. 8-2: Samantha K. and Kayla P. 8-3: Charles G. and Orlando O. 8-4: Hayden B. and Andrew J. 8-5: Tanya H. and Rebecca S. 8-6: Brandy C. and Ashley U. 8-7: Mitchell H. and Sarah L.

**8-1: Parallel and Perpendicular Lines**
Notes: [|Section 8-1 Student 1011.pdf] media type="custom" key="8956446" View the lesson:
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**Student Summaries:**

8-2: Solve Systems of Equations Graphically
Notes: [|Section 8-2 Student 1011.pdf] media type="custom" key="8970036"

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**Student Summaries:**

8-2 Summary In this lesson we learn about the system of equations, solution of a system, and how to graph the solutions and find where the two lines intercept eachother. A system of equations is where you have two or more equations with the same two variables that you solve at the same time. Also we learned about a solution to the system which is when two lines intersect to make the ordered pair become true. - Samantha K.

In this section we learned how to graph a system of equations to find the solution of the equations. The point where the lines intersect is the solution of the system of the equations. Before you graph you need to get both of the equations in the same form and then graph them on the graph to see where they intersect. -Kayla P.

8-3: Solve Systems by Substitution
Notes: [|Section 8-3 Student 1011.pdf] media type="custom" key="9012566" View the lesson:
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**Student Summaries:** Orlando O.: On this section we learned how to solve a system of a equation using substitution. Charles G.- if you have two equations and you solve for one and get that answer and plug that answer back in to the other equation and you get your answer for the equations and than check it. thats substitution.

8-4: Solve Systems by Adding, Subtracting, and Multiplying (Linear Combinations)
Notes: [|Section 8-4 Student 1011.pdf] media type="custom" key="9041902" View the lesson:
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**Student Summaries:** Hayden B.- In this lesson we learn how to solve systems by multiplying, subtracting, and adding. There are 5 steps. 1. Choose variable to eliminate 2. Make coefficients of variable opposite then combine them. 3. Solve for the remaining variable. 4. Plug back into an original equation to find the other variable. 5. Check and rewrite

Andrew J. - In this lesson titled solve systems by adding, subtracting and multiplying we learned how to solve systems of equations by adding or subtracting and to solve systems of equations by adding and multiplying. Things to remember are the addition property of opposites can help explore other ways to solve a system of equations. Also recall that the sum of opposites is always zero. Use the five step rule that we learned from the notes in section 8-4. 1. Choose a variable to eliminate. 2. If the coefficients of the variables in each equation are opposite already, you can add the two equations together. If the coefficients are not already opposites, multiply each equation to make the coefficients opposite, then add the equations together. 3. Solve the new equation for the variable that is left. 4. Plug the value for this variable back into one of the original equations and solve for the other variable. 5. Check the answer in the other equation and rewrite the answer as an ordered pair.

If you follow these simple five steps and practice them over and over again you should have no trouble solving systems by adding, subtracting, and multiplying. Also as a fun fact in the real world you may see this in landscaping, construction, and in a lot of sports.

8-5: Matrices and Determinants
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**Student Summaries:** What this section was about is Matrices and Determinants. Some of the vocabulary we had to define was: Square matrix, Determinant, and Cramer's Rule. Mostly what you do in this section is cross multiply. Also when you are finding the things to multiply always remember that Ax=Y values and the Ay=X values. - Tanya H.

8-5 goes over matrices and determinants. a Matrix is made up of rows and collumns and a determinant are the numbers that make up a matrix - Becca S.

8-6: Directed Graphs
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This section was based on figuring out how many ways you can get to a place with either one or no stops in between. Then you have to make a chart called a matrix which shows how many times you can get from one place to the other. This lesson is a good way to tell how many different ways you can do things and get to places with just reading a chart or looking at a picture. - Brandy
 * Student Summaries:**

This section is about Directed Graphs which is a geometrical representation of a map. A collection of points and arrows to show relations. - Ashley U.

8-7: Systems of Inequalities
Notes: [|Section 8-7 Student 1011.pdf] media type="custom" key="9142438" View the lesson:
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Section 8-7 teaches you how to write a system of linear inequalities for graphs and also how to graph a solution to a set of a system of linear inequalities. This lesson shows us that when two linear equations are graphed there will be the intersection of the area that are solutions for each. Also called a //Feasible Set//. (//Feasible Set- a solution to a system of linear inequalities)// Any ordered pair that is within one of these sets can be part of the overal solution. This is what we learned in section 8-7. --Sarah and Mitch
 * Student Summaries:**

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