What is the nature of solution if D = 0?

1.	What is the nature of solution if D = 0?
Answer» 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.

Answer»

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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