Wednesday, March 7, 2007

Unit 7 - "Special" Systems - No Solution? Many Solutions?

Questions on how to solve "special systems" - post them here!

7 comments:

Unknown said...

i cant figur out #23 rite now i got:

3pt pblms= x
5pt pblms= y
46 total pblms= 46
3x+5y=46 turns into
y=(-3/5)x+46/5

this shows up on the graf calc but i cant find the answer

Mr. Chamberlain said...

Good question... this is a common problem for developing algebra students!

You need to be more EXPLICIT in the definition of your variables.

x is the NUMBER OF 3-pt problems
y is the NUMBER OF 5-pt problems

46 is the total number of problems
150 is the total point value

SO...

what does 3x + 5y = ???

and further, can you now make an equation for:
x + y = ???

Hmmm... two equations? You got yourself a SYSTEM that you can solve!

Let me know how it works for you!

Daniel said...

Okay, Ryan the reason you cannot figure it out is because you are missing the other half of the system.

BUT FIRST, you need to redefine x and y. You should have x = # of 3-point problems and y = # of 5-point problems, and written this first equation, x+y=46. And you should understand that this is saying that the # of three point questions and the # of five point questions equals the # of questions total, which is 46.

So now to explain why 3x+5y=46 is wrong. So we know that x + y = the # OF PROBLEMS!!! so therefore 3x = the NUMBER OF POINTS YOU GOT FROM the 3-point (because it is 3 multiplied by the number of 3-pointers problems), and 5y= the NUMBER OF POINTS YOU GOT from the 5-point questions. So what you were saying in the statement 3x+5y=46 is that the number of points you got from the 3-pointers and the 5-pointers equals 46, which is incorrect. So you need to understand the context of the equations/systems you are writing.

So now that you know what the problem is with 3x+5y=46, we move onto your other problem. You see you only have half of the system here now with x+y=46. What you forgot was part of the problem was that the number of points the test is worth, 150. So this is where the "3x+5y=" comes in. So 3x+5y=150, and this means that three times the number of 3-point questions, and 5 times the number of 5-point questions, gives you the total number of points 150. SO NOW... after all of this you have to figure out the answer using the system below:
x+y=46xS
{ }
3x+5y=150
Sorry for being late on this, I meant to answer your question yesterday but the internet went crazy.
╟ §o §aid §ovalius╢

Daniel said...

Seems we crossed again Mr. Chamberlain.

╟ §o §aid §ovalius╢

Mr. Chamberlain said...

That's OK. I think your explanation gave just a tad more detail...

Unknown said...

Um Mr. Chamberlain your prob going to yel at me for this, but whatwas the hw last class. I was absent

InvAsian said...

There was no homework on Mar. 13 :D :D