MAT136 UToronto Mathematics Linear Equations Discussion Help

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Question Description

INSTRUCTIONS:

Choose one of the following two prompts to respond to. In your two follow-up posts, respond to one peer who picked the first prompt, and one peer who picked the second prompt. Use the discussion as a place to ask questions, speculate about answers, and share insights. Be sure to embed and cite your references for any supporting images.

  • Option 1: There are three ways to solve a system of equations: by elimination (sometimes called addition), by substitution, and by creating a graphical representation. Of these, which method is the best? Why? Consider possible advantages and disadvantages of each.
  • Option 2: When looking at two linear equations, how can you tell if the corresponding lines are parallel, the same line, or perpendicular? How many solutions does each possibility have, and why? Provide an example to support your statements. In your follow-up post, add an equation. What is the result?


NOTES TO TUTOR: I have attached the rubric for this question.. also, below is a post from one of my peers for prompt 2.. please reply.


PEER RESPONSE:

Hello everyone!

For this weeks discussion I will be covering prompt 2. When looking at two linear equations, you can tell the lines are parallel if the slope of the lines are the same. We can tell if they are perpendicular if one lines slope is opposite reciprocal to the other. We can tell two linear equations have the same line if both their slopes and y-intercepts are the same, or in other words the same equation. So lets say we have two equations, 1: Y=-2/3x + 3, 2: Y=2/3x + 6. These two equations would produce parallel lines because there slopes are the same. If the two equations were 1: Y=-2/3x +4 and 2: Y=-2/3x + 4, we know they are the same line because they are the same exact equation. Lastly, if we had two equations, 1: Y=-2/3x +4 and 2: Y= 3/2x + 4, we know these will be perpendicular because the slopes are opposite/inverse of each other. As far as solutions go, linear equations can have 0,1, or infinite solutions.

Best,

Matt

Unformatted Attachment Preview

Discussion Rubric: Undergraduate Your active participation in the discussion forums is essential to your overall success this term. Discussion questions are designed to help you make meaningful connections between the course content and the larger concepts and goals of the course. These discussions offer you the opportunity to express your own thoughts, ask questions for clarification, and gain insight from your classmates’ responses and instructor’s guidance. Requirements for Discussion Board Assignments Students are required to post one initial post and to follow up with at least two response posts for each discussion board assignment. For your initial post (1), you must do the following:  Compose a post of one to two paragraphs.  In Module One, complete the initial post by Thursday at 11:59 p.m. Eastern Time.  In Modules Two through Eight, complete the initial post by Thursday at 11:59 p.m. of your local time zone.  Take into consideration material such as course content and other discussion boards from the current module and previous modules, when appropriate (make sure you are using proper citation methods for your discipline when referencing scholarly or popular resources). For your response posts (2), you must do the following:  Reply to at least two different classmates outside of your own initial post thread.  In Module One, complete the two response posts by Sunday at 11:59 p.m. Eastern Time.  In Modules Two through Eight, complete the two response posts by Sunday at 11:59 p.m. of your local time zone.  Demonstrate more depth and thought than simply stating that “I agree” or “You are wrong.” Guidance is provided for you in each discussion prompt. Rubric Critical Elements Comprehension Exemplary Develops an initial post with an organized, clear point of view or idea using rich and significant detail (100%) Timeliness Engagement Writing (Mechanics) Provides relevant and meaningful response posts with clarifying explanation and detail (100%) Writes posts that are easily understood, clear, and concise using proper citation methods where applicable with no errors in citations (100%) Proficient Develops an initial post with a point of view or idea using adequate organization and detail (85%) Submits initial post on time (100%) Provides relevant response posts with some explanation and detail (85%) Writes posts that are easily understood using proper citation methods where applicable with few errors in citations (85%) Needs Improvement Develops an initial post with a point of view or idea but with some gaps in organization and detail (55%) Submits initial post one day late (55%) Provides somewhat relevant response posts with some explanation and detail (55%) Writes posts that are understandable using proper citation methods where applicable with a number of errors in citations (55%) Not Evident Does not develop an initial post with an organized point of view or idea (0%) Value 40 Submits initial post two or more days late (0%) Provides response posts that are generic with little explanation or detail (0%) Writes posts that others are not able to understand and does not use proper citation methods where applicable (0%) 10 Total 30 20 100% ...
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Tutor Answer

Tutornicabel
School: University of Maryland

Attached.

Running head: Linear equations

1

Linear equations
Name of student
Name of professor
Name of course
Name of institution

Linear equations

2

Option 1:
Methods of solving linear equations are of three types which include elimination, graphing and
substitution method (Golub, 1965). A linear equation is a system that involves two relationships
which has two variables in each relationship. Linear equation systems are solved by finding
where the two relationships are true or where the two lines cross one another (Campbell, 1980).
All three methods of solving linear equations give the same right answer but they have different
advantages and disadvantages.
Substitution method

This method involves substituting an expression from one equation for the variable in another
equation. This method is used when where at least one variable in one of the equations is
required to be isolated. The substitution method is useful when the equation has an isolated
variable or where a variable in an equation has a coefficient of one. The substitution method is
the best method for solving basic algebraic equations very quickly. Limitation of this method is
that it can lead to arithmetic mistakes while solving arithmeti9c equations.

Elimination method

This method is used to solve l...

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Review

Anonymous
Thanks, good work

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