Question

x-2y-5 =0 ,3x -6y=15​

Answer 1

There are infinite values of x and y ... No unique solution exist.

Answer 2

Here you go...

Solving:

The given system of equations:

x + 2y = 5

⇒ x + 2y - 5 = 0 ….(i)

3x + ky + 15 = 0 …(ii)

These equations are of the forms: a1x+b1y+c1 = 0 and a2x+b2y+c2

= 0

where, a1 = 1, b1= 2, c1 = -5 and

a2 = 3, b2 = k, c2 = 15

(i) For a unique solution, we must have:

this part in picture no.1

Thus for all real values of k other than 6, the given system of equations will have a unique solution.

(ii) For the given system of equations to have no solutions, we must have:

this part in picture no. 2

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