mat 116 Week 7 Discussion Questions
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mat 116 Week 7 Discussion Questions

Course Number: MTH/116 AAGN0BTWV3, Spring 2010

College/University: University of Phoenix

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Week 7 Discussion Questions 1. Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Graphing 1. Pro -you can see geometrically how solutions are found. 2. Pro- useful when approximate answers are needed. 3. Pro -We can solve inconsistent systems with graphs that are parallel lines and systems of dependent equations that are the same...

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7 Week Discussion Questions 1. Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Graphing 1. Pro -you can see geometrically how solutions are found. 2. Pro- useful when approximate answers are needed. 3. Pro -We can solve inconsistent systems with graphs that are parallel lines and systems of dependent equations that are the same line. 1. Con- If the solution does not involve integers or is too large to be seen on the graph, it is impossible to tell exactly what the solutions are. 2. It is difficult to accurately find a solution such as a fraction from a graph. Substitution 1. Pro- Gives exact solutions. 2. Pro - Easy to use if a variable is on one side by itself. 3. Pro- We can solve inconsistent systems with graphs that are parallel lines and systems of dependent equations that are the same line. 1. Cons- Solutions cannot be seen. 2. Cons- Can introduce extensive work with fractions when no variable has a coefficient of 1 or -1. Elimination 1. Pros- Gives exact solutions. 2. Pro- Easy to use if no variable has a coefficient of 1 or -1. 1. Con - Solutions cannot be seen. Which method do you like best? Why ? I like the substitution method the best because one equation is already solved, or can be solved quickly, for one of the variables. What circumstances would cause you to use a different method? When solving geometry or money problems using two or more variables When solving mixture problems using two variables. When solving distance-rate-time problems When solving a motion problem When solving a problem with three variables using a system of three equations You prefer substitution but you would use a different method for these circumstances: When solving geometry or money problems using two or more variables When solving mixture problems using two variables. When solving distance-rate-time problems When solving a motion problem When solving a problem with three variables using a system of three equations Do you know the method you would use for each circumstance? Well I have a feeling I responded to this question incorrectly. I think in some of the circumstances substitution could work just as well or in conjunction with that elimination method. But I believe some systems are easier to solve by elimination than by substitution. When solving geometry or money problems using two or more variables I believe the method I would use is elimination or substitution depending on the equation. When solving a mixture problem using two variables I would use the elimination method to solve the equations. When solving distance-rate-time (motion) problems I would apply the motion formula d=rt, and I would use the elimination/substitution method to solve. When solving a problem with three variables using a system with three equations that are called an ordered triple, I would use an extension of the elimination method. I would do this by going three from equations (eliminating a variable) to two equations (eliminating the same variable from any other two equations) to one equation (eliminating a second variable from the two equations in two variables from the first two steps). Once the last equation is solved, I would proceed to substitute this answer into a two-variable equation to find the value of the second variable. Finally, I would substitute the two values into a three-variable equation. I Consider responding to your classmates by indicating pros and cons they may not have considered or persuading them to see the value of the method you like best (if you chose different methods). Describe situations in which you might use their methods of solving. DQ 2 Post your response to the following: Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? The author decides how he will solve the word problems by using the information in the order it is presented. By following the order that the information is given in this helps the student to determine what the first and second equation will be along with what methods are needed to solve the system. What about the second equation? In this specific equation, the author determines how to solve the second equation simply by rearranging the outcome from the first equation. How are these examples similar? Both equations apply the substitution and elimination method when solving the system. All examples used a five-step method for solving the equations. These steps were familiarizing, translating, solving, checking, and stating. All the examples had at least one unknown variable. Both example problems two and three dealt with money in the equations. In addition, both example problems three and four used percentages, which need to be converted before the solution to the system, could be established. Also they both were mixture problems. How are they different? The circumstances of these examples were all different. In example two and four, we worked with and solved a mixture problem. However, example two was trying to determine how many packets of each type of garden seed should be put in the garden mix. Whereas, example four we were mixing two brands of fertilizers. Example #3 was a money problem. Lastly, all the examples had different solutions. Find a problem in the text that is similar to examples 2, 3, and 4. Post the problem for your classmates to solve. Student Loan Sarahs two student loans totaled $12,000. One of her loans was at 6% simple interest and the other at 9%. After one year, Sarah owed $855 in interest. What was the amount of each loan? Consider responding to your classmates by asking clarifying questions or by expanding a classmates response. Also, help students solve the problem you posted by providing feedback or hints if necessary. You may also want to provide an explanation for your solution after a sufficient number of students have replied.

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&=&=+=& & =&=== === & &=====!"#$% *%& &=+ "#= +' +$ ( $( #" %) ,= - + == = + ) =( )(. &% =-/ = , & = ( + & & &&== ( = = =)=1(0$%$$%)==& = ++ 1+=)$ 2 34$# 2) 2 35=& &$ 2 63578*" 8 -*
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