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in Negative Numbers and Integers by (46.9k points)
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What is the nature of solution if D = 0?

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If D = 0, i.e. a1b2 – b1a2 = 0, then the two simultaneous equations do not have a unique solution.

Examples:

i. 2x – 4y = 8 and x – 2y = 4

Here, a1b2 – b1a2 = (2)(-2) – (-4) (1)

= -4 + 4 = 0

Graphically, we can check that these two lines coincide and hence will have infinite solutions.

ii. 2x – y = -1 and 2x – y = -4

Here, a1b2 – b1a2 = (2)(-1) – (-1) (2)

= -2 + 2 = 0

Graphically, we can check that these two lines are parallel and hence they do not have a solution.

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