Question

the key to using the elimantion method is to find variable terms in the two equations that have unequal coefficients true or false?

Answer 1

would opposite coefficients be the same as unequal coefficients ?
For example : you would want 1 equation to have 4x and the other equation to have -4x, so that they can cancel each other out.

Answer 2

@amistre64 ....question for you ?

Answer 3

@whpalmer4 .....I have a question

Answer 4

you've got questions, we've got answers :-)

Answer 5

but first, often more questions to you :-)

Answer 6

are opposite coefficients the same as unequal coefficients ?

Answer 7

I think they are, but I want to confirm

Answer 8

well, I'm not sure what whoever is writing this considers "opposite".

the way I say it is that the magnitude needs to be equal, and the sign opposite.

so, 4 and -4 is a good matchup, because the magnitude of both is 4, and the sign is opposite.

4 and -3 is not a good matchup for doing elimination, because although the signs are opposite, the magnitude is not the same.

Answer 9

really, the key is that the magnitudes are equal. it doesn't matter if the signs are identical or opposite because you can either subtract or add to combine the equations.

Answer 10

it is perhaps easier if the signs are opposite, just because many people make fewer mistakes adding than they do subtracting, especially if negative numbers are involved.

Answer 11

so would you consider the answer to this question true or false ?

Answer 12

they are unequal

Answer 13

-4 is not equal to 4...right ?

Answer 14

although they are both 4 spaces from 0

Answer 15

I am just confused on the wording

Answer 16

I would consider it false, because you can eliminate with equal coefficients. Let me demonstrate:

\[2x + 3y = 5\]\[-2x + y = 7\]I can eliminate here by simply adding the two together:
\[(2-2)x + (3+1)y = 5+7\]\[4y=12\]

but what if I had \[2x + 3y =5 \]\[2x -y = -7\]
(the second equation is equivalent to the second equation of the first set, just multiplied through by -1)

Well, here I can subtract!
\[2x + 3y = 5\]\[2x-y=-7\]------------
\[(2-2)x + (3-(-1))y = 5-(-7)\]\[4y = 12\]
same result!

Answer 17

so, the key is that the magnitude was the same, not that the signs were opposite.

Answer 18

magnitude is just another word for absolute value in the case of a single number...

Answer 19

thanks because I was leaning towards true......I see the light...lol....

Answer 20

I prefer to do it by addition so I don't risk making mistakes doing subtraction of negative numbers. If I have to multiply one equation by -1 to make the signs opposite, I do so, that's easy.

Answer 21

the key to using the elimantion method is
to find variable terms in the two equations
that have unequal coefficients

not necessarily

Answer 22

personally, I'm not a fan of questions like this that perhaps are a better test of your ability to parse the question than your understanding of the underlying concept...

Answer 23

x + 3y = 6
x - 2y = 7

the xs have the same coeff, but its just as easily eliminated

Answer 24

thats true....multiplying by -1.....I understand now....the wording threw me off

Answer 25

not that parsing questions accurately isn't a valuable skill to develop, but presumably this is a math class, not a critical reading class :-)

Answer 26

thanks for explaining

Answer 27

you're welcome!

Answer 28

thank you everyone this really helped and i learned a few things too ^_^