# MAT136 UToronto Mathematics Linear Equations Discussion Help

__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