Question

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

Answer 1

First, convert the equations into slope intercept form.

$y=mx+b$

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

First equation :

$-2x+3y\geq -12 \\ 3y\geq-2x-12\\y\geq-\frac{2}{3}x-4$

Second equation :

$x+y<3\\y<-x+3$

So now we graph

$y<-x+3$ and $y\geq-\frac{2}{3}x-4$

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

Since $y\geq-\frac{2}{3}x-4$ 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.

Answer 2

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