Question

determine the value of k for which the given system of equations has infinite solutions .

x+ (k+1)y = 5

(k+1)x+9y =8k- 1

Answer 1

Dear Student,

x + (k+1)y = 5
​​​​​​(​k+1)x + 9y = 8k-1
As the system of equation has infinite many solutions, therefore
a1/a2=b1/b2=c1/c2
a1=1, b1=(k+1), c1=5
a2=(k+1), b2=9, c2=8k-1
by putting these values in the above equation we get
1/(k+1)=(k+1)/9=5/(8k-1)
on comparing any two values,
1/(k+1)=(k+1)/9
(k+1)2 = 9
k+1= +-$\sqrt{9}$
k+1 = +- 3​​​​
Case 1
k+1=3
k=2
Case 2
K+1=-3
k=-4

Regards