Question

some one plz help me
need help solve the system of equations by graphing then classify the system as consistent or inconsistent, and as dependent or independent 4x-y=15 x+5y=-12 step by step plz

Answer 1

These are linear equations in two variables
If they have a common solution, then they will cross each other at a point and hence will be consistent.
We put them in the form ax + by + c = 0
4x - y - 15 = 0 and
x + 5y + 12 = 0

Now If
a1/a2≠b1/b2

then they will intersect at one point and will have a unique and consistent solution
Here a1/a2 = 4/1 and b1/b2 = -1/5

Since a1/a2 is not equal to b1/b2, therefore it will have a unique solution and they are consistent.

Answer 2

Also since they share only one common point, they are consistent and independent

Answer 3

For your info,
if \[a1/a2 \neq b1/b2\] then they are consistent and independent as they will cut each other at one point

if \[a1/a2 = b1/b2 = c1/c2\] then they r consistent a dependent as the two lines will lie on each other

if \[a1/a2 = b1/b2 \neq c1/c2\] then they r independent as they r parallel lines and will not meet/cut each other at even one point

Hope this clears everything....

Answer 4

tina ????

Answer 5

im more confused

Answer 6

Why??

Answer 7

because i have no idea how to do this

Answer 8

the other guy is telling me one thing and someone else told me another

Answer 9

First you have to put the given equations in ax + by + c = 0 form
See how I did it....
Is that clear or not??

Answer 10

yes

Answer 11

ok so 4x-y+15=0?

Answer 12

No it will be - 15 becoz when you shift a term from one side to the other, its sign changes

Answer 13

So, it will be 4x -y - 15 = 0

Answer 14

ok and x+5y-12=0 for the second equation?

Answer 15

No, x + 5y + 12 = 0 as sign on - 12 will become + when it is shifted to the other side.

Answer 16

ok then what

Answer 17

Now we check what is the ratio of the coefficients of x in the two equations.
Here a1/a2 = 4/1 as in first eqn it is 4x and in the second eqn it is 1

Answer 18

Then we check for the ratio of the coefficients of the y in the two equations
Here b1/b2 = -1/5 as in first eqn it is -y and in second eqn it is 5y

Answer 19

Finally we check for the ratio of the constant terms in the two equations
here c1/c2 = -15/12

Answer 20

Clear till now??

Answer 21

nope lost me when you started talking about ratio's 5y

Answer 22

U u/sttod a1/a2 = 4/1 ??

Answer 23

yes it is 4x

Answer 24

I guess it wud be easier if cud talk, do u hv a SKYPE account???

Answer 25

I hv a SKYPE id hakki.singh

Answer 26

not anymore

Answer 27

well it wud hv been very easy if we cud talk.....

Answer 28

i dont remember any of this from the hmwk

Answer 29

Maybe u are being taught a different method, mine is very simple and easy to follow if u get the hang once

Answer 30

x=0
then y=

Answer 31

No, first u hv to look at the coefficients of the x terms of both equns
In the first one 4 is the coefficient of the term 4x
In the second one 1 is the coefficient of the term x

Answer 32

Clear??

Answer 33

ok

Answer 34

So, a1/a2 ie the ratio of the coefficients of the x terms of the first eqn and the second eqn is 4/1

Answer 35

clear??

Answer 36

ok

Answer 37

Now we go the y terms

Answer 38

In the first eqn it is -y and in the second eqn it is 5y
so b1 is -1 abd b2 is 5
so b1/b2 is -1/5

Answer 39

clear??

Answer 40

ok

Answer 41

Finally we look at the constant terms
Here it is -15 in the first eqn and 12 in the second eqn

So, c1/c2 is -15/12

Answer 42

Clear??

Answer 43

ok

Answer 44

Now we have to understand the terms consistent/inconsistent and dependent/independent

Answer 45

consistent means that the two eqns share at least one or more solutions
This means that if their graphs cut each other at one point or the two lines coincide in which case they share infinite solutions

inconsistent means that they do not share even one solution i.e. the line never meet

Answer 46

Got it??

Answer 47

yes

Answer 48

And in case they r consistent i.e they share one or more solutions, then they will be independent if they share just one solution and dependent if they share many solutions ie.e the line coincide

Answer 49

So we can have
consistent and dependent
consistent and independent and
inconsistent

Answer 50

Clear??

Answer 51

it is only one answer and the solution of the system typed in an ordered pair,

Answer 52

I'm coming to the solution, but is the above classifications as consistent and dependent, consistent and independent and inconsistent clear??

Answer 53

yes

Answer 54

Fianlly,
if
a1/a2≠b1/b2
then they are consistent and independent as they will cut each other at one point

if
a1/a2=b1/b2=c1/c2
then they r consistent a dependent as the two lines will lie on each other

if
a1/a2=b1/b2≠c1/c2
then they r inconsistent as they r parallel lines and will not meet/cut each other at even one point

Answer 55

In your case a1/a2 = 4/1 and b1/b2 = -1/5

So, a1/a2 is not equal to b1/b2, so your pair of equations is consistent and independent

Answer 56

Clear??

Answer 57

yes

Answer 58

So, it is now clear tht yr system of pair of eqns is consistent and independent.

To draw their graphs, you modify the first equation by separating x and y as follows
4x - 15 = y
Now put various values like -1 , 0, 1, 4 for x and getting corresponding values of y

Understood??

Answer 59

yes

Answer 60

Similarly modify the second eqn as follows:
5y = -x -12 (remember signs change when you shift their side)
so,
-x -12
y = -----------
5

Now, put various values for x and calculate corresponding values of y.

Now plot the graphs for the two eqns separately and you will find them cutting each other at one point.

Answer 61

Clear????

Answer 62

Your intersection point shud b (3, -3)

Answer 63

Hope now everything is clear??

Answer 64

ok and it is consistent and independent

Answer 65

yes it is

Answer 66

ok ty so much for all your help I really appreciate it

Answer 67

U r welcome.
In this we have to be clear what consistent/inconsistent and dependent/independent mean.
Then using the three ratio checks we can find whether there will be one solution, many solutions or no solution.

Do I get a medal for this??