- anonymous

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

- chestercat

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- anonymous

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.

- anonymous

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

- anonymous

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....

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- anonymous

tina ????

- anonymous

im more confused

- anonymous

Why??

- anonymous

because i have no idea how to do this

- anonymous

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

- anonymous

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

- anonymous

yes

- anonymous

ok so 4x-y+15=0?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

ok then what

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Clear till now??

- anonymous

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

- anonymous

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

- anonymous

yes it is 4x

- anonymous

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

- anonymous

I hv a SKYPE id hakki.singh

- anonymous

not anymore

- anonymous

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

- anonymous

i dont remember any of this from the hmwk

- anonymous

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

- anonymous

x=0
then y=

- anonymous

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

- anonymous

Clear??

- anonymous

ok

- anonymous

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

- anonymous

clear??

- anonymous

ok

- anonymous

Now we go the y terms

- anonymous

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

- anonymous

clear??

- anonymous

ok

- anonymous

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

- anonymous

Clear??

- anonymous

ok

- anonymous

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

- anonymous

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

- anonymous

Got it??

- anonymous

yes

- anonymous

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

- anonymous

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

- anonymous

Clear??

- anonymous

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

- anonymous

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

- anonymous

yes

- anonymous

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

- anonymous

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

- anonymous

Clear??

- anonymous

yes

- anonymous

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??

- anonymous

yes

- anonymous

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.

- anonymous

Clear????

- anonymous

Your intersection point shud b (3, -3)

- anonymous

Hope now everything is clear??

- anonymous

ok and it is consistent and independent

- anonymous

yes it is

- anonymous

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

- anonymous

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??

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