Question

The system, 6x - 4y = 5 and 9x - 6y = 5, is consistent.
True
False

Answer 1

its false right?

Answer 2

do you know what is consistent and inconsistent ?

Answer 3

yes but u can describe it further :)

Answer 4

but for that you have to describe how much you know first ? :)

Answer 5

all i know is that its a system

Answer 6

A system is consistent if it has atleast one solution.
A system is inconsistent if it has no solutions.

Answer 7

thx ash :)

Answer 8

Just adding to that abstract definition it's really the concept of geometry of straight line in a plane.

Answer 9

as far your question goes ..

Answer 10

yeah, if you plot these two equations, you'll get two lines which don't intersect, that's why there is no solution
if the lines intersect there is a solution

Answer 11

what she meant is this two are parallel lines hence they would never intersect.

Answer 12

i hate plottinglol

Answer 13

but why ?

Answer 14

not she, he :D

Answer 15

Oh sorry :D

Answer 16

no problem

Answer 17

math was never my gift...:(

Answer 18

Change them to slope-intercept form:
6x - 4y = 5 add 6x to both sides
-4y = -6x + 5 divide both sides by -4
y = (-6)/(-4)x - 5/4 simplify
y = 3/2x - 5/4

Now the other equation:
9x - 6y = 5 subtract 9x from both sides
-6y = -9x + 5 divide by -6
y = (-9)/(-6)x -5/6 simplify
y = 3/2x -5/6

Now let's compare the SLOPES and the INTERCEPTS of
y = 3/2x - 5/4 and
y = 3/2x -5/6

They have the SAME slope (3/2) so they are PARALLEL
they have DIFFERENT y-intercepts (-5/4) and (-5/6) respectively.

So that means the lines are parallel and do not overlap.

=================
The system is INCONSISTENT.
=================

You can see this by going to http://www.wolframalpha.com and typing

plot 6x - 4y = 5 and 9x - 6y = 5

Hope this helps!

Answer 19

hey lisa math can be learnt by practice :)

Answer 20

omg that really help!

Answer 21

ash: this is my second year repeating algebra :(

Answer 22

There are other tricky ways in linear algebra that could solve this task just by seeing the equation.

Answer 23

for example just consider the ratio of the two coefficients they are equal but not equal to the ratio of the constants hence inconsistent.

Answer 24

lisa: don't be upset, work hard and u'll pass with flying colors

Answer 25

thx ash :)... the first semester is almost over and i dont even have half of my work done lol

Answer 26

and again just try to find the determinant of the coefficient matrix you will see that this is a singular and hence the system is inconsistent.

Answer 27

foolformath thx for the information <3

Answer 28

how old are you lisa ?

Answer 29

17

Answer 30

you are welcome ..

Answer 31

cool you have lots of time to learn mathematics :)

Answer 32

lisa it's never too late to start right now

Answer 33

thx guys :)... i just hope to graduate by next year...im home schooled..

Answer 34

wow !! that's even better .. just remember that mathematics couldn't be learned unless you are in love with it .. it's a beautiful subject just need a little bit of you attention and care .. treat it like your boyfriend :P and it will love you back :D

Answer 35

lol thats good advice :) haha

Answer 36

hehe :D :)

Answer 37

so r u a teacher?

Answer 38

me?

Answer 39

both of you :)

Answer 40

no i'm just a graduate , working now, will go for post graduation in a year or so

Answer 41

I am just another student who is a fool :P

Answer 42

haha you guys are cool!....

Answer 43

stay hungry stay foolish :D

Answer 44

hehe :D but I love to eat btw :P

Answer 45

Maths graduate ash ?

Answer 46

nope , engineering graduate :D

Answer 47

hahah who doesnt like to eat? but i recently became a vegetarian its hardlol

Answer 48

duh not good :P.. what's up with you girls ?? My gf too become veggie :(

Answer 49

that's good lisa, i'm also a vegetarian . never tasted meat or anything like that

Answer 50

Veggie ?? how can you live without that? :P

Answer 51

well i watched this show about meat and it was talkin about how meat is causeing cancer....and thats cool ash! :)

Answer 52

well ur gf is a smart girl :)

Answer 53

yeah ur gf is smart, u should learn from her

Answer 54

Sorry, I can't give up meat .... my body and mind refuses to work without it .. :P

Answer 55

I know she is smart.. how else I would be dating her ? :P hehe :D

Answer 56

yeah :D

Answer 57

lol she has a smart boy friend ;) but he needs to give up meat loljk

Answer 58

i just broke up with my boy friend.. he was jerklol

Answer 59

I am no near to be smart .. I am just a FOOL :P

Answer 60

oh you'd fine a better guy soon :D

Answer 61

and I am sorry hear that lisa . :(

Answer 62

ffm ur being modest

Answer 63

lisa and foolformath what's the time there

Answer 64

:)...its ok....i finally realized i dont need him.

Answer 65

thx

Answer 66

I am not ash, you don't know how much I have to work to remember simple things :anybody who works like me would do much better .. I believe

Answer 67

lisa you are 17 .. boys will come and boys will go .. do not worry :)

Answer 68

ffm well whatever it take u still r smart :) and thx...i just hope i dont keep getting hurt... it sucks lol

Answer 69

keep practicing you'd be able to remember more :)

Answer 70

I know the feeling .. I was once dumped like that :P but you know then I met the most beautiful thing Mathematics .. now we are together forever :D

Answer 71

easy to say than done :P

Answer 72

yeah lisa, i also hope so, may u get a guy who cares for you the most

Answer 73

lol aww u really do have a passion for math..thats awsome

Answer 74

aww thx ash :)

Answer 75

btw i didnt get dumped...lol

Answer 76

fool for math that's very cool.

Answer 77

oh yes only guys get dumped :P hearless girls ..... :D

Answer 78

jokes :D

Answer 79

lol i know :D

Answer 80

i don't know that, never been dumped, with my girl since2 years

Answer 81

wow ash thats cool! u two must really love eachother:)

Answer 82

the longest iv been with a guy is 4 months

Answer 83

wow excellent track record lisa :P

Answer 84

that happens in this age, u enjoy and live it to the fullest, won't get this time again

Answer 85

lol ;)

Answer 86

yea but i wish i was older already

Answer 87

you know i'd also wished this, but now i feel that time was much better

Answer 88

lol yea... btw i miss public school...but i got in trouble alote.....lets just say the wrong crowd

Answer 89

public school ? it's good ? ??

Answer 90

well i liked it cause i loved being wit my friends everyday.... now i barely see them

Answer 91

oh lisa that's sad:(

Answer 92

that's sad ..

Answer 93

hey foolfor math what's ur name

Answer 94

I have never studied in public school myself so I really don't know but they say it's not good..

Answer 95

I am Max :)

Answer 96

cool name

Answer 97

My full name is Maximus Decimus Meridius! guess who I am :P

Answer 98

haahah :D..