In respect of the equation `[{:(2,3),(4,6):}][{:(x),(y):}]=[{:(" "5),(c-5):}]`
correctly match List I with List II and select the correct answer using the code given below the lists :
`{:(,"List I","List II"),(,("Value of c)"),("Nature of the Equation")),(A.,5,1."The equation has no solution."),(B.,10,2. "The equation has a unique solution."),(C.,15,3. "The equation has an infinite set of"),(,," ""solution."),(,,4. "The equation has two infinite sets of"),(,," ""independent solution"):}`

Options

A. `{:(A,B,C),(4,2,3):}`
B. `{:(A,B,C),(1,1,3):}`
C. `{:(A,B,C),(2,2,4):}`
D. `{:(A,B,C),(4,1,3):}`

Answer

B

Explanation

`[{:(2,3),(4,6):}][{:(x),(y):}]=[{:(5),(c-5):}]rArr[{:(2x + 3y),(4x + 6y):}]=[{:(5),(c-5):}]`
`rArr 2x + 3y = 5" "...(1)`
and `4x + 6y = c - 5" "...(2)`
`rArr` Soloving equation (1) and (2) c = 15
Now, if c = 15, equations 1 and 2 becomes
`rArr 2x + 3y = 5 and 4x + 6y = 10`
This shows that the equation has an infinite set of solutions. For other values of c, equation has no solutions.