mayankdevnani
  • mayankdevnani
Given: 3x-4y=7 and x+cy=13 , for what value of "c" will the two equations not have a solution?
Mathematics
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SOLVED
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katieb
  • katieb
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mayankdevnani
  • mayankdevnani
options are : a) \[\frac{3}{4}\] b)\[\frac{4}{3}\] c) \[-4\] d) \[\frac{-4}{3}\]
hartnn
  • hartnn
i think there is easier way out....
ash2326
  • ash2326
Rewrite first equation \[x-\frac{4}{3}y=7\] for no solution we need to have parallel lines second equation \[x+cy=13\] compare this with the first \[c=-\frac{4}{3}\]

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More answers

hartnn
  • hartnn
^^ exactly
ParthKohli
  • ParthKohli
@hartnn: Oh yeah
anonymous
  • anonymous
WELL FOLLOW @ash2326 THAT ONE MUCH EASIER..... agreed with @hartnn
hartnn
  • hartnn
no solution is of the form: ax+b=c ax+b=d
ParthKohli
  • ParthKohli
Yes.
mayankdevnani
  • mayankdevnani
@ash2326 gd and then
Zarkon
  • Zarkon
and why would that have an infinite # of solutions?
hartnn
  • hartnn
because ax+b=c and ax+b=c are satisfied by infinite number of points (x,y) simultaneously.
Zarkon
  • Zarkon
ash2326's solution is mostly correct
Zarkon
  • Zarkon
this one doesn't satisfy that
mayankdevnani
  • mayankdevnani
ok! then @Zarkon
Zarkon
  • Zarkon
3x-4y=7 and x+cy=13 \[x-\frac{4}{3}y=\frac{7}{3}\] \[x+cy=13\]
mayankdevnani
  • mayankdevnani
yaa ... i also agree with @Zarkon don't you @mathslover
Zarkon
  • Zarkon
if c=-4/3 then you get \[x-\frac{4}{3}y=\frac{7}{3}\] and \[x-\frac{4}{3}y=13\] ie \[\frac{7}{3}=13\]
Zarkon
  • Zarkon
thus no solution
mayankdevnani
  • mayankdevnani
isn't like this \[3x-4y=7\] \[3x=7-4y\] \[x-y=\frac{7}{12}\] \[x=\frac{7}{12}+y\]
mayankdevnani
  • mayankdevnani
and then solve it
mathslover
  • mathslover
What I did is this : \[\large{7+4y = 3(13-cy)}\] \[\large{7+4y=39-3cy}\] \[\large{32= 4y+3cy}\] We have to find the value of c when the RHS becomes zero which will give no solution. \[\large{4y+3(c)(y)=0}\] \[\large{c = \frac{-4y}{3y}}\] \[\large{c=\frac{-4}{3}}\] hence at c = -4/3 we get no solutions for the variables in the given two equations .
anonymous
  • anonymous
@mayankdevnani what r u doing?
mathslover
  • mathslover
@mayankdevnani you need to concentrate hardly on understanding questions... You are solving for x or y but in the question we have to find the value for c which makes the solutions for the equation as null set.
mayankdevnani
  • mayankdevnani
how did you get it......... @mathslover
mathslover
  • mathslover
btw , @Zarkon sir , was my method acceptable? I know there are easy methods too.. but that is what I did..
mayankdevnani
  • mayankdevnani
ANSWER is correct... but i did'nt understand..... plz tell me once again.....
mathslover
  • mathslover
@mayankdevnani where are you not getting ?
mayankdevnani
  • mayankdevnani
step by step
anonymous
  • anonymous
THAT WAS exactly what I was thinking @mathslover THAT IS ABSOULETLY CORRECT
Zarkon
  • Zarkon
yes...your way is fine
mathslover
  • mathslover
OK thanks @sauravshakya Let us wait for honorable zarkon sir ..
mathslover
  • mathslover
OK thanks a lot @Zarkon .. that fine made a lot sense sir.. :)
mayankdevnani
  • mayankdevnani
@mathslover how did you get it \[7+4y=1(13-cy)\]
ghazi
  • ghazi
-4/3
mayankdevnani
  • mayankdevnani
ya.. but how??
ghazi
  • ghazi
that will be a prallal line
mathslover
  • mathslover
3x-4y = 7 x = (7+4y) / 3 and then : x + cy = 13 x = 13-cy 13-cy = (7+4y)/3 (since they are equal to x) 3(13-cy) = 7+4y
mathslover
  • mathslover
got it @mayankdevnani ?
ghazi
  • ghazi
just put -4/3 at C and you will have a parallel set of line and parallel set of lines have no solution
ghazi
  • ghazi
@mayankdevnani clear?
mayankdevnani
  • mayankdevnani
ok... @mathslover
ghazi
  • ghazi
3x-4y=7 and 3x-4y=39 are parallel lines how could they have a solution ..they intersect nowhere
ghazi
  • ghazi
neither do they overlap
mayankdevnani
  • mayankdevnani
thnx.... @Zarkon @ghazi @sauravshakya @ash2326 but special thnx to @mathslover
ghazi
  • ghazi
:)
ghazi
  • ghazi
@mathslover is my approach correct?
anonymous
  • anonymous
Isnt your method same as @ash2326 's method........ @ghazi
ghazi
  • ghazi
i didn't see ...i just came here read the question and identified these are parallel lines...i guess yes both have same solution and we don't need to solve anything because already it is visible that it's case of parallel line when c= -4/3 hence no solution
ghazi
  • ghazi
yes it is similar to that of @ash2326

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