Question

How do you graph the system of linear inequalities `2x+y<6` and `y> -2`?

Answer 1

`2x+y<6` and `y > -2`
First consider the related linear equations:
`2x+y=6 rarr y = -2x+6`
and
`y = -2`

`y = -2x+6`
is a line with y-intercept at `(0,6)` and a slope of `(-2)` (which means that for every unit increase in `x`, `y` decreases by `2`)

`y=-2`
is a horizontal line through the point `(0,-2)`

It is fairly simple to plot these lines;
then we just need to determine which sides of these lines need to be combined for the given inequalities
Since
`y>-2`
the points of the Range must be above the horizontal line

Since
`2x+y<6`
the points of the Range must be below the line for `2x+y=6` (since if `y_1` is in the Range and `y_2<y_1` then `y_2` must also be in the Range).