For what value of k will the following pair of linear equations have infinitely many solutions kx+3y

This video is only available for Teachoo black users

Page 2

Last updated at Dec. 18, 2020 by Teachoo

This video is only available for Teachoo black users

Solve all your doubts with Teachoo Black (new monthly pack available now!)

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.

Text Solution

Solution : as we know that `a_1x+b_1y+c_1 = 0` <br> `a_2x+b_2y+c_2=0` <br> has infinity solutions only when <br> `a_1/a_2 = b_1/b_2 = c_1/c_2` <br> so here, `k/12= 3/k = -(k-3)/(-k)` <br> `k/12= 3/k` <br> `k^2 = 36` <br> `k= +-6` <br> case 1 : `6/12=3/6=-(6-3)/(-6)` <br> `1/2=1/2=1/2` <br> case 2: `k=-6` <br> `-6/12=3/-6=-(-6-3)/-(-6)` <br> `-1/2=-1/2 = -(-9)/(-(-6)=3/2` <br> `=-1/2=-1/2=3/2` false statement<br> `:.` k = 6 answer

Text Solution

Solution : Comparing the given equations with <br> `a_(1)x + b_(1)y + c_(1) = 0` <br> and `a_(2)x + b_(2)y + c_(2) = 0` <br> We have <br> `(a_(1))/(a_(2)) = (k)/(12), (b_(1))/(b_(2)) = (3)/(k)` and `(c_(1))/(c_(2)) = (-(k + 3))/(k)` <br> Now, for coincident lines <br> `(a_(1))/(a_(2)) = (b_(1))/(b_(2)) = (c_(1))/(c_(2))` <br> implies `(k)/(12) = (3)/(k) = - ((k+3))/(k)` <br> `{:("Taking first two expressions, we get"),((k)/(12) = (3)/(k)" ...(1)"),(implies" "k^(2) = 36),(therefore " "k = pm 6 ):}:|{:("Taking last two expressions, we get"),((3)/(k) = - ((k + 3))/(k)" "...(2)),(implies " "3k = - k^(2) - 3k),(implies " "k^(2)+ 6k = 0 ),(implies " " k(k + 6) = 0),(therefore " k = 0 or k = - 6 "):}` <br> But k = - 6 is a value which satisfies both the equations (1) and (2). <br> `therefore` k = - 6

For what value of ' K ' will the following pair of linear equations have infinitely many solutions Kx +3 y = k 3 ; 12 x + ky = k[ or k x+3 y k+3=0 ; 12 x+k y k=0]

Open in App