Which one of the following options is true, and why?
has
(i) A unique solution (ii) Only two solutions (iii) Infinitely many solutions
Answer:
Every linear equation consisting of two variables has infinite many solutions. Therefore, equation
also has infinite many solutions. Hence, the answer is (iii).
This is because after putting random value of
in the equation, we get one unique value of y. Or, by putting random value of
in the equation, we get one unique value of
.
Let’s take an example:
When I put
in the given equation
, we get
Therefore, (0, 5) is one of the infinite solutions.
When I put
in the given equation
, we get
Therefore, (1,8) is also one of the infinite solutions.
In the same way, we can put any random value of
in the equation and can find corresponding value of
.
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