Question

Find the values of 'a' such that system 2x+3y+5z=0, 7x+3y-2z = 1,
2x+3y+az=1 has i) No solution
Unique solution.​

Answer 1

2x+3y+5z=9,

7x+3y−2z=8,

2x+3y+λz=μ

Now, for infinitely many solutions. If 2 equations out of 3 are same then we are left with only 2 equations with 3 variables, this will give infinite solutions. Now if λ=5, μ=9, then equation (i) and (iii) will be same and the system will have infinite solutions.

Hence, B is correct.