Answer:
Option D.
Step-by-step explanation:
Consider option D. [tex]y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3[/tex]
Take point (0,0)
On putting this point in inequation [tex]y\leq \frac{3x}{4}+10[/tex] , we get
[tex]0\leq 10[/tex] which is true . So, solution is region towards the origin i,e region below the line [tex]y= \frac{3x}{4}+10[/tex] including the line itself .
On putting (0,0) in inequation [tex]y\leq \frac{-x}{2}-3[/tex] , we get [tex]0\leq -3[/tex] which is false , so solution is region away from the origin i.e region below line [tex]y= \frac{-x}{2}-3[/tex] including the line itself .
So, common solution to both the inequations is the shaded part in the given figure .
In other words, we can say that the graph shown in the given figure represents system of equations: [tex]y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3[/tex]
