Question

for what value of k will the following system of equation have infinitely many solutions

$2x + 3y = 4$

Answer 1

Step-by-step explanation:

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