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Linear Inequalities — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLinear Inequalities1 Mark
MCQ
Inequations involved in the given region are$...........?$
  • A
    $2\text{x}+\text{y}\geq6,\text{x}\geq0,\text{y}\geq0$
  • B
    $2\text{x}+\text{y}>,\text{x}\geq0,\text{y}\geq0$
  • C
    $2\text{x}+\text{y}<6,\text{x}\geq0,\text{y}\geq0$
  • ✓
    $2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$
✓

Answer

Correct option: D.
$2\text{x}+\text{y}\leq6,\text{x}\geq0,\text{y}\geq0$
Since region involves $1^{st}$ quadrant so $\text{x}\geq0,\text{y}\geq0.$
Two points on line are $(0,6)$ and $(3,0)$
$\frac{(\text{y}-6)}{(0-6)} =\frac{(\text{x}-0)}{(3-0)}$
$\Rightarrow\frac{(\text{y}-6)}{(-6)}=\frac{\text{x}}{3}$
$\Rightarrow\text{y}-6=2\text{x}$
$\Rightarrow2\text{x}+\text{y}=6$
$2\text{x}+\text{y}\leq6$ since $(0,0) $ should also satisfy.
So, $ 2\text{x}+\text{y}\leq6, \text{x}\geq0, \text{y}\geq0.$

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