Question

What is the value of k .For which the simultaneous equation 2x+3y=8 and 6x-ky=24 have infinitely many solutions? options are as follows
A) 6
(B) -6
(C)9
(D) -9
Please... give me answer

Answer 1

Answer:

d)-9 is the solution of this question

Answer 2

find value of 'k' for which the given equations have infinite solutions

Explanation:

1. let there be a pair of simultaneous equations in variables x and y,                          $a_1x+b_1y+c_1=0\\a_2x+b_2y+c_2=0$                                                                                                        where $a_1,a_2,b_1,b_2,c_1\ and\ c_2$ are real numbers.    
2. then these simultaneous equations will have infinitely many solutions only if they satisfy the given below condition,                                                                                                                                                                                                 $\frac{a_1}{a_2} =\frac{b_1}{b_2} =\frac{c_1}{c_2}$         ----(a)
3. given simultaneous equations , $2x+3y-8=0,\ \ \ \ \ 6x-ky-24=0$                  we have,  $a_1=2,\ a_2=6\ \\b_1=3,\ b_2=-k\ \\c_1=-8,\ c_2=-24$    
4. putting these values in (a) we get,   $\frac{2}{6} =\frac{3}{-k}= \frac{-8}{-24}$                                                         hence, $k=-3(3)\ \ \ \ \ \ \ \ ->k=-9$   ----->ANSWER