No wonder students are having so much trouble learning math. This is a very confusing method of teaching the elimination method.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.
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.
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
Well I’m not a mathemetician but multiplying the first equation by 3y gets you -3y doesn’t it?
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.
Apparently, there is one *best* way to solve any algebra homework problem. Post it on the Internet (e.g. Yahoo Answers).
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
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)
Substitution method is easiest.
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
Only multiplying the first equation by 3 will work. Work it out and you will see why.
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.
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?
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?
Everyone can argue all they like at how to answer this.
However, those six words were placed there by someone who doesn't know how to ask a question, unless they were looking for a "gotcha" response, or for students to parrot back exactly what they were taught without the students actually thinking for themselves.
As a NYC public high school Algebra teacher, I can definitively state that the "best possible" first step, is the one that makes the most sense to you, which will also yield the correct answer.
What’s the point of this kind of question? Multiple choice in Algebra? What about just “Solve for X and Y”? And this is supposed to be Algebra 2?
This kind of stuff was first semester Algebra 1 when I was in middle school. And no one would have asked a multiple choice question about selecting the best first step - we just had to solve for the variables.
There are 2 ways to solve this problem: substitution or elimination. Evidently, the test makers do not want the student to consider the substitution method.
As for the question asked, I would use option A. Negative 3 ( -3) requires merely one step. Option C, a positive 3, ( +3), would require the extra step of having to multiply by negative 1 ( -1).
The Postmodernism that is now the paradigm in the public schools since the Fabian socialists redesigned curricula in the 30’s is intentionally designed to destroy logic and reason to their irrational thinking—Marxism.
In other words, the Baconian/Newtonian world (Modern Philosophy) that was the basis of reason and logic for our country in the first 200 years is being systematically destroyed.
Destroy knowledge and rational thinking with cognitive dissonance and rubbish and emotional issues to destroy intellectual excellence and all ability to come to rational answers.
Marxism needs to have irrational thinkers who are unable to spot the Big Lie.
They believe things like up is down, homosexual activity is a “good”.
All kids should be taken out of public schools and all textbooks designed for public education need to be burned. Really.
Create a Blue Ribbon Panel to study how this makes Americans feel.
Math education stinks these days. They have eliminated most of the common sense and straight-forward ways of doing things, have 4th graders doing variables, etc. They have also made a real push to make it apply to real life, to answer the whine, ‘Why do I have to do MATH?” Instead of just saying, “Because ....”
I am tutoring a kid this summer who is so confused by 4th grade math that he is getting a D. Smart kid. Guess what? They are teaching ‘a different way,’ designed by some bachelor PhD guy at some university. I suggested that I teach ‘real math’ this summer to the child, so he would have a solid foundation on which to build ‘designer math’ next fall. The teachers don’t usually understand the Designer Math approaches, either, because they don’t make sense, so they cannot teach them adequately.
Mom would not hear of it — ‘He must learn how to do it their way, so he can get an A.” Forget whether or not it made sense to the kid.
// rolling eyes//
First of all, you are right in that choices A and C are both correct.
But do not be too quick to blame the teacher. In the school district were I live, teachers MUST teach the one method approved by central administration and teach that method only.
And, no, I'm not exaggerating. Every course has a handbook which must be followed to the letter. A first deviation will result in a warning. If the teacher continues ANY deviation from the handbook, the district will begin dismissal proceedings.