This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
Total Pageviews
Thursday, February 10, 2011
hw #6-3 Solving Systems Using the Elimination Method aka Linear Combinations Method
Archibald argues that this method should really be called the "Elimination by Linear Combinations" Method. Agree/ Disagree?
I was having trouble with question #3b in the packet. When I substituted for both equations to check my work, I ended up with different answers. For 2x+3y=17 I gotsk y = -16.33. For x+3y=16 I gotsk y = -5.66. Please let me know what you got for each one. Thanks
Your first step should have been to SUBTRACT the second equation from the first equation... in essence you are subtracting 16 from both sides. On the right side, you are CLEARLY subtracting 16 and on the left side, you are subtracting (x+3y) which, in YOUR PATHETIC LITTLE WORLD, is ALWAYS equal to 16, yes?
2x-x=x 3y-3y=0 17-16=1
Therefore, x=1!!
Ca-peesh?? ... but are you done? NO!!! You need to identify the y- coordinate as well.
[for anonymous at 11:12] I didn't find a formula, but I found trying the two closest numbers that add up is a good place to start (4 and six is a better start for ten than 9 and 1)
On the Diamond Problems, you're trying to get the "#" spaces to equal the sum (on the bottom) when added together, and also equal the product (at the top) when multiplied together.
Diamond problems should be FUN for you excellent mathematical types! You are trying to find two numbers that SUM to one number and MULTIPLY to the other. The product is "north" the sum is "south" and since addition and multiplication are BOTH COMMUTATIVE (you knew that), the order of the left and right numbers (whether addends or factors) doesn't matter!
You're trying to find two numbers that add to the bottom number and multiply to the top.
My question is for #30. How would you set up a system of equations for the pizza? I tried to, but somehow got that a ham and pineapple pizza would have -16 calories.
I can't be sure, but I think you are trying to solve the systems individually. NO, NO, NO!!
You are simply using the POE's (Properties of Equality) to manipulate the equations.
In this case, if you add or subtract the equations as-is, you won't eliminate a variable. A good first step is to multiply the second equation by 5, that will give you the "new" system:
Dear Monty Python (6b #10), What don't you know (the # of days, right?) What is the rate of change (per day) in each situation? How do you represent the starting quantities for each situation graphically?
well gosh, it's a good thing we have an actual class!! And that you can come in for extra help (tomorrow 7am work for you?)
Remember, the solution to a system of LINEAR equations is the point(s) where they intersect. The possibilities are that: 1) the lines intersect in a single point 2) the lines are parallel (no intersection, no solution) 3) the lines are the same line (many/infinite solutions)
Ohh okay.. So the amount of food they start out with is the y intercept. Gotsk it! For the slope of the equation, would it then be for example -10x (x being each day passing) ?
#4 on 377 is asking you to identify and describe one of the methods we use to solve systems of equations. We have learned to 1) graph systems 2) use the substitution method 3) use the elimination (aka linear combinations) method
Which method are they describing in question #4? Explain your answer. Why does it work? You start out with two equations in two unknowns (variables) and end up with how many equations in how many unknowns?
We will discuss this and other exciting questions (have you ever met an algebra question that wasn't exciting?) in class tomorrow. I just spent 21 hours of my weekend in class myself... I'm going to sleep!!
... sprinkle a little POE on those babies and they'll match up like spaghetti and meatballs! I'll even let you use a calculator (although a true algebra-tician would refuse the offer!).
I was having trouble with question #3b in the packet. When I substituted for both equations to check my work, I ended up with different answers. For 2x+3y=17 I gotsk y = -16.33. For x+3y=16 I gotsk y = -5.66. Please let me know what you got for each one. Thanks
ReplyDeletesame problem with 4b
ReplyDeleteWith 3b, the system was:
ReplyDelete2x+3y=17
x+3y=16
what was your first step?
Your first step should have been to SUBTRACT the second equation from the first equation... in essence you are subtracting 16 from both sides. On the right side, you are CLEARLY subtracting 16 and on the left side, you are subtracting (x+3y) which, in YOUR PATHETIC LITTLE WORLD, is ALWAYS equal to 16, yes?
ReplyDelete2x-x=x
3y-3y=0
17-16=1
Therefore, x=1!!
Ca-peesh??
... but are you done? NO!!! You need to identify the y- coordinate as well.
Get to work!
Now you can walk me thru 4b, k?
ReplyDeleteIs there supposed to be a specific formula to figure out the diamond problems, other than trial & error?
ReplyDeleteAlso having trouble with 4b.. I got the coordinate pair (11,-9) but when I went to check with the second equation (x-3y=20) I got 38=20 :O
ReplyDelete[for anonymous at 11:12] I didn't find a formula, but I found trying the two closest numbers that add up is a good place to start (4 and six is a better start for ten than 9 and 1)
ReplyDeletewhat are you actually trying to figure out on the diamond problems?
ReplyDeleteTrouble figuring out equations for #10 in Problem set 6B..
ReplyDeleteOn the Diamond Problems, you're trying to get the "#" spaces to equal the sum (on the bottom) when added together, and also equal the product (at the top) when multiplied together.
ReplyDeleteDiamond problems should be FUN for you excellent mathematical types! You are trying to find two numbers that SUM to one number and MULTIPLY to the other. The product is "north" the sum is "south" and since addition and multiplication are BOTH COMMUTATIVE (you knew that), the order of the left and right numbers (whether addends or factors) doesn't matter!
ReplyDeleteUSE YOUR MATHEMATICAL INTUITION... NO FORMULAS!!
You're trying to find two numbers that add to the bottom number and multiply to the top.
ReplyDeleteMy question is for #30. How would you set up a system of equations for the pizza? I tried to, but somehow got that a ham and pineapple pizza would have -16 calories.
Dear 4b,
ReplyDeleteI can't be sure, but I think you are trying to solve the systems individually. NO, NO, NO!!
You are simply using the POE's (Properties of Equality) to manipulate the equations.
In this case, if you add or subtract the equations as-is, you won't eliminate a variable. A good first step is to multiply the second equation by 5, that will give you the "new" system:
7x+15y=32
5x-15y=100
Can you tell me what to do next?
In the last explanation, I should have capitalized the word SIMPLY. K.I.S.S., k?
ReplyDeleteDear Monty Python (6b #10),
ReplyDeleteWhat don't you know (the # of days, right?)
What is the rate of change (per day) in each situation?
How do you represent the starting quantities for each situation graphically?
Let me know how you do... k?
Dear Pizza,
ReplyDeleteI don't have the book with me, so you'll have to 'splain the problem better.
i dont understand this at alllllll.....any of it and i am so frustrated...i have read everything and i still dont understand it
ReplyDeletewell gosh, it's a good thing we have an actual class!! And that you can come in for extra help (tomorrow 7am work for you?)
ReplyDeleteRemember, the solution to a system of LINEAR equations is the point(s) where they intersect. The possibilities are that:
1) the lines intersect in a single point
2) the lines are parallel (no intersection, no solution)
3) the lines are the same line (many/infinite solutions)
See you at 7?
Let me know!
For 4B, you add them together?
ReplyDeleteyes...see you at seven.
ReplyDeletethanks.
ReplyDeleteYes, in 4b you add the equations, after you multiply the second (both sides of course) by 5.
ReplyDeletePOE POE POE me!
Oh never mind I guess I made a stupid mistake! I gotsk it!
ReplyDeleteOhh okay.. So the amount of food they start out with is the y intercept. Gotsk it! For the slope of the equation, would it then be for example -10x (x being each day passing) ?
ReplyDeleteAm I going in the wrong direction..? For 10b in the problem Set 6B I got y=1000, does it sound wrong?
ReplyDeleteI don't understand what #4 in the textbook on pg 377 is trying to ask..
ReplyDeleteDear Misunderstood,
ReplyDelete#4 on 377 is asking you to identify and describe one of the methods we use to solve systems of equations. We have learned to
1) graph systems
2) use the substitution method
3) use the elimination (aka linear combinations) method
Which method are they describing in question #4? Explain your answer. Why does it work? You start out with two equations in two unknowns (variables) and end up with how many equations in how many unknowns?
We will discuss this and other exciting questions (have you ever met an algebra question that wasn't exciting?) in class tomorrow. I just spent 21 hours of my weekend in class myself... I'm going to sleep!!
Goodnight!!
Mr. C.
Ok.. Thanks for the help!
ReplyDeleteCan't WAIT for more exciting questions!!
I guess I'll wait 'til tomorrow to ask about #30. (Pizza Problem)!
ReplyDeleteGood night
Dear Ham & Pepperoni,
ReplyDelete.5p + .75h = 765
.25p + h = 745
... sprinkle a little POE on those babies and they'll match up like spaghetti and meatballs! I'll even let you use a calculator (although a true algebra-tician would refuse the offer!).
Good Night (and I mean it this time!)
Mr. C.
Nighty Night!
ReplyDelete(But I have more questions.. See you tomorrow!!) >:) <- That's an evil face