Question

Any solution of the linear equation 2x+0y=9 in two variables, is of the form:
$
  (a){\text{ }}\left( {\dfrac{9}{2},0} \right) \\
  (b){\text{ }}\left( {\dfrac{9}{2},n} \right),n{\text{ is a real number}} \\
  (c){\text{ }}\left( {0,\dfrac{9}{2}} \right),{\text{ n is a real number}} \\
  (d){\text{ }}\left( {n,\dfrac{9}{2}} \right) \\
 $

Answer 1

Hint – In this question solve the equation for the value of x. Now as the coefficient of y is zero so no matter what the value of y may be this term will always be zero. Use this concept to get the right ordered pair depicting the value of x and y.

Complete step-by-step solution -
Given linear equation is
$2x + 0y = 9$
As we see that the coefficient of y is zero so the multiplication of zero with any variable is also a zero.
So above equation is written as
$ \Rightarrow 2x = 9$
Now divide by 2 we have,
$ \Rightarrow x = \dfrac{9}{2}$
So one of the solutions of the given linear equation is (9/2).
Now y can be any real number because when we multiply any real number to zero the resultant is zero.
$ \Rightarrow y = n$, Where $n \in R$
So any solution of the linear equation is $\left( {\dfrac{9}{2},n} \right)$, n is a real number.
Hence option (B) is correct.

Note – A real number includes all the rational numbers such as integer as well as fractions, and all the irrational numbers as well. 0 is also a real number, that is why the value of y is taken as a real number ranging from $ - \infty {\text{ to + }}\infty $.