For what value of k does the system of equationsx + 2y = 3, 5x + ky + 7 = 0have (i) a unique solution, (ii) no solution?Also, show that there is no value of k for which the given system of equations has infinitely many solutions.

(i) Given: x + 2y = 3 – eq 1

5x + ky + 7 = 0 – eq 2

Here,

a1 = 1, b1 = 2, c1 = - 3

a2 = 5, b2 = k, c2 = 7

Given systems of equations has a unique solution

k ≠10

k ≠ 10

(ii) Given: x + 2y = 3 – eq 1

5x + ky + 7 = 0 – eq 2

Here,

a1 = 1, b1 = 2, c1 = - 3

a2 = 5, b2 = k, c2 = 7

Given that system of equations has no solution

=

Here,

=

Here,

k = 10

k = 10

For the system of equations to have infinitely many solutions

= =

= = which is wrong.

That is, for any value of k the give system of equations cannot have infinitely many solutions.

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