Question

Select the graph that represents the system of inequalities below.

Answer 1

The given inequalities are

`y\leq-(1)/(2)x+3\text{ and }y>(1)/(2)x+1`
`\text{Substitute x=2 in y=}-(1)/(2)x+3\text{ as follows.}`

`y=-(1)/(2)(2)+3=-1+3=2`

The point is (2,2) lies in the given first inequality.

`\text{Substitute x=2 in y=}(1)/(2)x+1\text{ as follows.}`

`y=(1)/(2)(2)+1=1+1=2`

The point is (2,2) lies in the given second inequality.

Hence the point of intersection is (2,2).

Option D is the only graph that shows the point of intersection is (2,2).