Question

1. graph the system of inequalities
-2x+3y≥ -12
x+y< 3

Answer 1

the answer is y> -2/3+2x/3

Answer 2

First, convert the equations into slope intercept form.

`y=mx+b`

Where m is the slope and b is the y intercept.

First equation :

`-2x+3y\geq -12 \\ 3y\geq-2x-12\\y\geq-(2)/(3)x-4`

Second equation :

`x+y<3\\y<-x+3`

So now we graph

`y<-x+3` and
`y\geq-(2)/(3)x-4`

Since
`y<-x+3` is less than and not equal to, we shade below the line and the line is dotted.

Since
`y\geq-(2)/(3)x-4` is greater than and equal to, we shade above the line and the line is solid.

And the solutions are anything in the double shaded region.