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

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nimit sharma

Answer 2

for infinite solution we need A1/b1=A2/b2=C1/C3
equation 1. 2x+3y=4
2x+3y-4=0
here A1=2 b1=3 and C1=-4
equation 2. (k+2) x +6y =3k+2
(k+2)x+6y-3k-2
here b1=(k+2) , b2= 6 and C3=-3k-2
so, 2/k+2=3/6= 2/k+2 should be equal to 1/2
k = 2 then 2/4 =1/2=1/2
hence the value of k = 2

hope it helps !!