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Q.
The area enclosed by $2|x|+3|y| \leq 6$ is
Straight Lines
Solution:
The given inequality is equivalent to the following system of inequalities.
$2 x+3 y \leq 6, $ when $ x \geq 0, y \geq 0 $
$2 x-3 y \leq 6, $ when $ x \geq 0, y \leq 0$
$-2 x+3 y \leq 6, $ when $ x \leq 0, y \geq 0$
$-2 x-3 y \leq 6, $ when $ x \leq 0, y \leq 0$
which represents a rhombus with sides
$2 x \pm 3 y=6 $ and $ 2 x \pm 3 y=-6$
The lengths of the diagonals are $6$ units and $4$ units, respectively, along the $x$ - and $y$-axes. Therefore, the required area is $1 / 2 \times 6 \times 4=12$ sq. units.
