On this page you will find some material about Lesson 2. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 2: 2-D Systems of Equations & Substitution and Elimination
- Know what it means to be a solution to a system of equations.
- Know how to verify a proposed solution.
- Explain the graphical approach to solving a 2-D linear system and explain each case.
- Explain the algebraic methods to solving a 2-D linear system.
- Use creativity to solve problems.
- Communicate effectively using written and oral means using logical thinking.
Topic. This lesson covers
Section 3.2: Solving Systems of Linear Equations by the Substitution Method,
Section 3.3: Solving Systems of Linear Equations by the Addition Method,
Section 3.4: Applications of Systems of Linear Equations in Two Variables.
WeBWorK. There is one WeBWorK assignment on today’s material:
Video Lesson 2 (based on Lesson 2 Notes)
These are questions on fundamental concepts that you need to know before you can embark on this lesson. Don’t skip them! Take your time to do them, and check your answer by clicking on the “Show Answer” tab.
This is like a mini-lesson with an overview of the main objects of study. It will often contain a list of key words, definitions and properties – all that is new in this lesson. We will use this opportunity to make connections with other concepts. It can be also used as a review of the lesson.
A Quick Intro to 2-D Systems of Equations & Substitution and Elimination
Key Words. Linear equation, system, solution, substitution, elimination, graph.
In a system of two linear equations in two variables, we consider two linear equations
Graphically speaking, this system consists of two lines.
A solution to the system must satisfy all equations at the same time. This means that the solution belongs to each line, so it is in the intersection of the two lines. This is the graphing method for obtaining the solution.
How many solutions can there be? There are three possible situations:
- the two lines intersect at one point; in this case, the system has only one solution, which is the intersection point.
- the two lines are parallel; in this case, the system has no solution.
- the two lines coincide; in this case, the system has infinitely many solutions.
There are two algebraic methods for solving a system of two linear equations.
Substitution Method: this method consists of isolating one of the variables from one of the equations, and substituting it into the other equation.
Addition Method: this method consists in multiplying each equation by a number (if necessary) so that when the two equations are added the resulting equation depends on one variable only.
Many times the mini-lesson will not be enough for you to start working on the problems. You need to see someone explaining the material to you. In the video you will find a variety of examples, solved step-by-step – starting from a simple one to a more complex one. Feel free to play them as many times as you need. Pause, rewind, replay, stop… follow your pace!
A description of the video
In the video you will see the following system
Now that you have read the material and watched the video, it is your turn to put in practice what you have learned. We encourage you to try the Try Questions on your own. When you are done, click on the “Show answer” tab to see if you got the correct answer.
You should now be ready to start working on the WeBWorK problems. Doing the homework is an essential part of learning. It will help you practice the lesson and reinforce your knowledge.
It is time to do the homework on WeBWork:
When you are done, come back to this page for the Exit Questions.
After doing the WeBWorK problems, come back to this page. The Exit Questions include vocabulary checking and conceptual questions. Knowing the vocabulary accurately is important for us to communicate. You will also find one last problem. All these questions will give you an idea as to whether or not you have mastered the material. Remember: the “Show Answer” tab is there for you to check your work!
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