Question

Which point is in the solution set of the given system of inequalities 3x+y>-3,x+2y<4

Answer 1

The closest answer is B. -2,0

Answer 2

Step 1. Solve both inequalities for
`y`:

`3x+y\ \textgreater \ -3`

`y\ \textgreater \ -3x-3`


`x+2y\ \textless \ 4`

`2y\ \textless \ -x+4`

`y\ \textless \ - (1)/(2) x+2`

Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines
`-3x-3` and
`- (1)/(2) x+2`:


`y=-3x-3` (1)

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

Replace (1) in (2):

`-3x-3=- (1)/(2) x+2`
Solve for
`x`:

`(5)/(2) x=-5`

`x=-2` (3)

Replace (3) in (1):

`y=-3x-3`

`y=-3(-2)-3`

`y=6-3`

`y=3`

We can conclude that the point (-2,3) is in the solution of the system if inequalities; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.