Math education today (vanity)

Yahoo Answers ^ | 06/10/11 | self

[Bob]

I just answered a question on Yahoo Answers which really makes me wonder about the current state of math education.

Here's the question:

ALGEBRA 2 HELP !!!!!!?

1. Select the best possible first step to solving the system by first eliminating the y variable.
5x - y = 5
7x - 3y = -1

A) Multiply the first equation by -3.
B) Multiply the second equation by -3.
C) Multiply the first equation by 3.
D) Multiply the second equation by 3.
(more at link)

[Bob]

Here's my answer:

No wonder students are having so much trouble learning math. This is a very confusing method of teaching the elimination method.

For the elimination method, the first step is to get either one of the variables to have the same coefficient in both equations, regardless of their signs.

1. Either answer A or C will work fine.

Multiplying equation 1 by -3 gets you -3y in it which matches the 3y in equation 2.

Multiplying equation 1 by 3 gets you 3y in it which again matches the 3y in equation 2.

If the signs are opposite, you can add the equations. If the signs are the same, you can subtract them.

2. Any of the first three answers will result in a 6x term in both equations.

3. Again, multiplying the first equation by 3 (whether +3 or -3) gets you matching coefficients of 3 for the x term.

Am I wrong in thinking that this student's teacher may only know one way to solve this type of problem? Throwing signs into the multiplication seems to add a totally unneeded confusion factor into the process.

[Mr. K]

A

Then you get a +3y and a -3y

Next, you subtract the first equation from the second

The +3y and -3y = 0 and so you are left with an easily solvable equation for x alone

[bkepley]

Well I’m not a mathemetician but multiplying the first equation by 3y gets you -3y doesn’t it?

[Eldon Tyrell]

You are incorrect -

The first step is to isolate the variable.

Y= mX + b

Then substitute this equation for Y into the second equation.

Multiplying first is needless complication. Also - it starts “blending” information from the two equations too early. No need to blend.

From your note - apparently there is a LOT of confusion.

[bkepley]

The test did not say it was the best method, just to show how it would be done if it was done this way. It’s a test of being able to add (or subtract) equations I guess.

[bkepley]

>Well I’m not a mathemetician but multiplying the first equation by 3y gets you -3y doesn’t it?

Meant to say multiplying the first equation by 3 gets you -3y.

Answer is A.

[USFRIENDINVICTORIA]

Apparently, there is one *best* way to solve any algebra homework problem. Post it on the Internet (e.g. Yahoo Answers).

[DFG]

The Yahoo solution makes this problem much harder than it really is.

1) Multiply the first equation by -3 and leave the second equation alone to get the following:

-15X + 3Y = -15
7X - 3Y = -1

2) Add these two equations together to get:

-8X = -16

3) Solve for X:

X = 2

4) Substitute X = 2 into either equation and solve for Y:

(7 x 2) - 3Y = -1
Y = 5

[Mr. K]

C would not wor

5x - y = 5
7x - 3y = -1

Line 1 time -3

-15x +3y = -15
7x _3Y = -1

Add them

-8X = -16

x = 2

so....

5x - y = 5
7x - 3y = -1

5(2) - y = 5
7(2) - 3y = -1

10 -y = 5 (subtract 5 from both sides, and add y to both)
14 -3y = -1 ( add 1 to each side and ad 3y to each side)

10 -5 = y
14 + 1 = 3y

5 = y
15 = 3y

x = 2
y = 5

CHECK: (ALWAYS DO THIS!!!!!!!!!!!!!!!)
5x - y = 5
7x - 3y = -1

5(2) - 5 = 5
7(2) - 3(5) = -1

10 - 5 = 5 (correct)
14 - 15 = -1 (correct)

[avacado]

Substitution method is easiest.

[Eldon Tyrell]

My point is - whoever wrote it - does not have a conceptual feel for math.

It jumps off the page - the first thing they do is start blending info brtween the two equations.

This may work for this simple example - but add another few terms, maybe another variable - etc - and see where you end up -

Also - makes it very hard to check the work. if first equation is modified to Y = mx+b - you can easily check that the answer holds - rather than having to check large multiples etc.

The goal should be to simplify - the test method complicates.

[Bob]

Either A or C will work.

Multiplying by 3 gets you:

15x - 3y = 5
7x - 3y = -1

Subtracting them gets you:

15x - 3y = 5
-(7x - 3y = -1)
-----------------
8x = 6

Multiplying by -3 gets you:

15x - 3y = 5
-7x + 3y = 1

Adding them gets you:

15x - 3y = 5
+(-7x + 3y = 1)
-----------------
8x = 6

[darkwing104]

There is no "best way" as it depends on who is teaching the subject and what are their desired result. There are several methods that can be employed to answer this correctly and all are valid.

[Mr. K]

oops

you are right that A and C are equally easy (for me and you) but I always think of ADD by default

mult. by 3 and subtract 2 from 1 (to most people) might be thought of as less “easy” as multiple by -3 and add

[JRios1968]

Only multiplying the first equation by 3 will work. Work it out and you will see why.

[JRios1968]

Make that -3 (minus 3)

[Bob]

You are incorrect -

The first step is to isolate the variable. Y= mX + b

No, you are incorrect. The question is to pick the first step for the elimination method, not the substitution method.

From your note - apparently there is a LOT of confusion.

How so?

[CriticalJ]

As a former high school math teacher and a part-time math instructor at the local community college, I can say with much confidence that students are getting worse at math, that most math text books are horrible, and that most students, administrators,and parents don’t give a damn as long as the students pass the class with an A or high B.

[blueunicorn6]

3 is a number. Y is a letter. Red is a color, but orange is a fruit. Is it any wonder the kids are screwed up?

[Bob]

(sorry, correction to my previous post)

Multiplying by 3 gets you:

15x - 3y = 15
7x - 3y = -1

Subtracting them gets you:

15x - 3y = 15
-(7x - 3y = -1)
-----------------
8x = 16

x = 2

---------------------------------

Multiplying by -3 gets you:

-15x - 3y = -15
-7x + 3y = -1

Adding them gets you:

-15x - 3y = -15
+(-7x + 3y = -1)
-----------------
-8x = -16

x = 2