Question

How do you follow the system of inequalities `-y \leq 3x + 4` and `- 3x + 3y \leq - 9`?

Answer 1

First bring the inequalities to standard form:
`y + 3x + 4 >= 0` (1)
`3y - 3x + 9 <= 0` (2).
Next, graph the Line (1) y + 3x + 4 = 0 by its intercepts.
Make x = 0 --> y-intercepts = - 4
Make y = 0 --> x-intercept = `- 4/3`
Then, graph the Line (2) 3y - 3x + 9 = 0 by its intercepts.
Make x = 0 --> y-intercept = - 3
Make y = 0 --> x-intercept = 3
The solution set of inequality (1) is the area above the Line (1).
The solution set of inequality (2) is the are below the Line (2).
The solution set of the system is the commonly shared area of the 2 solution sets.
Note. Both the 2 Line (1) and (2) are included in the system' solution set.
graph{y + 3x + 4 = 0 [-20, 20, -10, 10]}
graph{3y - 3x + 9 = 0 [-20, 20, -10, 10]}