How many linear equations in x and y

Question:

How many linear equations in x and y can be satisfied by x = 1 and y = 2?

(a) Only one            

(b) Two          

(c) Infinitely many            

(d) Three

Solution:

(c) Let the linear equation be ax + by + c = 0.

On putting x = 1 and y = 2, in above equation we get

=s a + 2b + c = 0, where a, b and c, are real number

Here, different values of a, b and c satisfy a + 2b + c = 0. Hence, infinitely many linear

equations in x and yean be satisfied by x = 1 and y = 2.

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