Question

If $2x + 3y = 24$ and $2x - 3y = 12$, then the value of $xy$ is________.
${\text{A}}{\text{.}}$10
${\text{B}}{\text{.}}$12
${\text{C}}{\text{.}}$18
${\text{D}}{\text{.}}$14

Answer 1

Hint: This question has a pair of linear equations in algebraic form so simply solving it by elimination method i.e. eliminating one variable either $x$ or $y$.

Complete step-by-step answer:

Let $2x + 3y = 24$ as first equation

And $2x - 3y = 12$ as second equation

adding both the equations we get the result as:
$
  4x = 36 \\
  x = \dfrac{{36}}{4} \\
  x = 9 \\
$

Now next step is putting the value of $x$ in either equation first or second, suppose we put it in first one then:

$
  2x + 3y = 24 \\
  2 \times 9 + 3y = 24 \\
  18 + 3y = 24 \\
  3y = 6 \\
  y = 2 \\
$

therefore, the value of $x$ is 9 and $y$ is 2 .
thus, value of $xy = 9 \times 2 = 18$

Note: In this type of question consisting of a pair of linear algebraic equation first make the coefficient of any of one variable same and then simply apply the elimination method through which we will get the value of one variable by eliminating other one and finally put the resulted value in any of the equation to get the final required result.