Question

What are the classifications of each system?

A. consistent independent
B. coincident
C. inconsistent

1. 4x-2y=10
2x-y=5

2. y=2x-3
-2x+y=-5

3. 2x-5y=14
3x+4y=10

4. y=4x-3
12x-3y=9

Answer 1

it worked :)

Answer 2

the first thing we need to do is to know what the definitions for ABC are in order to apply them

Answer 3

I know what they are
consistent independent- one solution
coincident-infinite solutions
inconsistent- no solutions

Answer 4

now, this question assumes you know how to see the properties of a line from the equations

if one equation can be multiplied to get the other equation, then they are the same line

if one equation can be multiplied to get the other equation (EXCEPT for the constant), then they are parallel lines

if neither of these hold, then they have to cross at 1 point

Answer 5

This I learned today, but I just don't know what the equations are, like what the equation is in line form.

Answer 6

lets take the first one, and test it out

4x - 2y = 10
2x - y = 5

in order to get the equations looking somewhat the same, then 2x times something has to equal 4x ... would you agree that multiplying the bottom by 2 would accomplish this?

Answer 7

Yes, I would.

Answer 8

So would it be A?

Answer 9

4x - 2y = 10
2(2x - y = 5)


4x - 2y = 10
4x - 2y = 10 they are the same equation, therefore the same line coincident

Answer 10

y=2x-3
-2x+y=-5

i would suggest getting all the x and y parts to the same side, what do we get from that?

Answer 11

y=2x-5

Answer 12

getting them both in y= form .. thats fine to :)

y=2x-3
y=2x-5

so, are they the same? or do they differ only by the constant? or neither?

Answer 13

3 and 5 so, they differ by the constant

Answer 14

then they are the same line, but in different positions ... which option is it?

Answer 15

I think C

Answer 16

parallel lines, so yes .. they have no points in common

Answer 17

2x-5y=14
3x+4y=10

try this one out ...

Answer 18

Perhaps B

Answer 19

show me your 'proof" try to turn one into the other ... or at best one variables coeff into the other

Answer 20

Well, I don't think you can turn one into the other

Answer 21

i dont think so either, but its fun to try :)

3(2x-5y=14)/2
3x+4y=10

3(x-5/2y=7)
3x+4y=10

3x-15/2y=21
3x+4y=10

you cannot change one into a multiple of the other so they are neither parallel or coincident they must have only 1 point in common

Answer 22

y=4x-3
12x-3y=9

you know the drill by now i hope :) see if we can change it

Answer 23

So a?

Answer 24

I'm not sure, but i think 12x-3=9 is like this in this problem -12x+9

Answer 25

1. same line, same constant, coincident lines
4x-2y=10
2x-y=5

2. same line, different constants, parallel lines
y=2x-3
-2x+y=-5

3. neither parallel or consistent ... crossing lines
2x-5y=14
3x+4y=10

Answer 26

y=4x-3
12x-3y=9

get all the x y parts to the same side

-4x+ y= -3
12x -3y=9

multiply thru by -3 and compare

Answer 27

I'm not sure how to do that

Answer 28

you are not sure how to multiply by -3?

Answer 29

no what to multiply -3 by

Answer 30

-4x+ y= -3
12x -3y=9
^
^
we have a -3y down here and should prolly have
a -3y up top as well

Answer 31

multiply the top part by -3

Answer 32

So it would be identical to the other equation

Answer 33

yes

Answer 34

so if they are the exact same does that make it B?

Answer 35

A. consistent independent , crossing lines
B. coincident , identical
C. inconsistent , off by a constant

yes, B :)

Answer 36

okay thanks!:)

Answer 37

youre welcome

Answer 38

Bye, Have a Great Rest of Your Day!:)