Question

For what value of k, will the following system of linear equations have infinitely many solutions? 2x +3y = 4 and (k+2) x +6y = 3k + 2.

Answer 1

here is your answer by Sujeet,
For infinitely many solution ,we must be have
a1/a2=b1/b2=c1/c2
putting value,
2/k+2=3/6=4/3k+2
2/k+2=1/2. or 1/2=4/3k+2
k+2=4. or 3k+2=8
k=4-2. or 3k=8-2
k=2. or. 3k=6
or k=6/3=2

then,
value of k=2


That's all

mark brainliest

Answer 2

Hey Mate ,

Here is the answer ,
______________________________________________________________

For infinitely many solutions : 
 a₁  =  b₁  =  c₁ 
 a₂      b₂      c₂

=>   2     =    3   =     -4   
     k+2         6      -(3k+2)

=>   2    =  1 
     k+2      2

=>  4 = k+2
=>  k = 2

Also we can check by putting it in this,

 1   =      4     
 2       3*2 + 2

=>  1  =  4 
      2      8

=>  1  =  1 
      2      2

Hence, k = 2.
______________________________________________________________
Hope this helped you !!
Please mark as brainliest !!