Question

The graph below shows the solution to which system of inequalities?

Answer 1

Option D.

Explanation:

Consider option D.
`y\leq (3x)/(4)+10\,,\,y\leq (-x)/(2)-3`

Take point (0,0)

On putting this point in inequation
`y\leq (3x)/(4)+10` , we get

`0\leq 10` which is true . So, solution is region towards the origin i,e region below the line
`y= (3x)/(4)+10` including the line itself .

On putting (0,0) in inequation
`y\leq (-x)/(2)-3` , we get
`0\leq -3` which is false , so solution is region away from the origin i.e region below line
`y= (-x)/(2)-3` 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:
`y\leq (3x)/(4)+10\,,\,y\leq (-x)/(2)-3`