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Linear inequalities with $2$ variables are of the form $Px + Qy \leq K\; \text{or} \; Px + Qy \geq K$ for some constants $P$ and $Q.$

  1. is an equality.
  2. is not linear since the power of $x$ and $y$ are not $1.$
  3. it is a linear inequality.
  4. not linear.

So, the correct answer is (C).

edited by
7 votes
7 votes

For any equation to be unequal, it cannot hold the symbol '='. So option 'a' and 'b' are out of the race. Now, option 'c' and 'd' are unequal. They had to be proved linear. To be linear, at most the degree of the variable can be 1. Option 'c' has abx+a2y≥15. Here x is of degree1 and 'y' is also of degree 1. Hence, it is linear. Option 'd' has xy+ax≥20, where 'x' and 'y' are on the same side making the degree 2 and hence it can't be linear.

 

So, Option C is the answer as it satisfies both linearity and inequality.

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