Question

For water values of k the system of linear equations 2x+5y=k, kx+15y=18 has infinitely many solutions?

Answer 1

2/k=5/15=K/18
THIS IS BECAUSE IT HAS INFINITY SOLUTIONS
NOW: 15×2=5K
30=5K
K=6

Answer 2

Hey mate..
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Given,

2x + 5y = K......(1)

Kx + 15y = 18.....(2)

From Eq. (1) and eq.(2) we get,

a' = 2 ; b' = 5 ; c' = K

a" = K ; b" = 15 ; c" = 18

We know that,

For a pair of linear equations to have infinitely many solutions , it should be in the form :-

a' / a" = b'/b'' = c'/c"

=> 2/K = 5/15 = K/18

=> 2/K = 1/3 = K/18

=> 2/K = 1/3

=> 6 = K

SInce, the value of K is 6.

Thus,

The system of the given linear equation will have infinitely many solutions when, the value of K = 6

Hope it helps !!☺