Question

Find the values of k for which the system will have (i) a unique solution, and (ii) no solution. Is there a value of k for which the system has infinitely many solutions?

2x + ky = 1
3x − 5y = 7

Answer 1

GIVEN:

To find: To determine for what value of k the system of equation has

(1) Unique solution

(2) No solution

(3) Infinitely many solution

We know that the system of equations

(1) For Unique solution

Here,

Hence for the system of equation has unique solution

(2) For no solution

Here,

Hence for the system of equation has no solution

(3) For infinitely many solution

Here,

But since here

Hence the system does not have infinitely many solutions.