Question

find the value of ‛k’ for which the following systems of linear equation has infinite number of solutions:2x+ky=3,(k+5)x+25y=2k+5.

Answer 1

Answer:

 The given equations has infinite no of solutions

Than

a1/a2=b1/b2=c1/c2

2/k+5=k/25=3/2k+5

taking a1/a2=b1/b2

2/k+5=k/25

50=k(k+5)

50=k^2+5k

k^2+5k-50=0

k^2+10k-5k-50

k(k+10)-5(k+10)

(k-5)(k+10)

k=5,-10