question_answer

Find the area of the region bounded by the system of linear equations \[x-y\text{ }1\text{ };\,\,\,\,2x+y=8\]and y axis.

A)  \[13\] square units         

B)  \[13.5\] square units

C)  \[14\] square units         

D)  \[14.5\] square units

Correct Answer: B

Solution :

\[\frac{1}{x}+\frac{y}{(-1)}=1\]            ?..(i) \[\Rightarrow \,\,\,\,\,\frac{x}{4}+\frac{y}{8}=1\]             ?.. (ii) From eq. (i) & (ii)- \[x-y=1\] \[\frac{2x+y=8}{3x=9}\Rightarrow x=3\Rightarrow CD=3\] Area of \[\Delta ABC=\frac{1}{2}\times 9\times 3\] \[~=\frac{27}{2}~=\underline{\mathbf{13}\mathbf{.5~square units}}\]