Question

Find the value of K for which the system 2x+3y-7 =0 and (K-1)x+(K+2)y-3K=0 has infinite solution.

Answer 1

`2x+3y - 7 = 0->(1)`
`(K-1)x+(K+2)-3K = 0`
For, these two equations to have infinite solutions,
`(K-1)/2 = (K+2)/3 = (-3K)/-7`
`=>(K-1)/2 = (K+2)/3`
`=>3K-3 = 2K+4`
`=> K = 7`
Now, `(K-1)/2 = (-3K)/-7`
`=>7K-7 = 6K`
`=>K = 7`
`:.` For `K = 7`, these equations will have infinite solutions.