Question

How do you solve the system of inequalities `x+ y \geq - 2` and `3y + 15x \leq 6`?

Answer 1

After transposing and simplification:
`y >= - x - 2` (1)
`y <= - 3x + 2` (2)
First, graph the Line (1) y = - x - 2 by intercepts -->
x = 0 --> y = - 2
y = 0 --> x = - 2
Next, graph Line (2) y = -3x + 2 by intercepts
x = 0 --> y = 2
y = 0 --> `x = 2/3`.
The solution set of Line (1) is the area above this line. Color it
The solution set of Line (2) is the area below this line. Color it.
The common solution set of the system is the commonly shared area of the 2 solution sets. Color it. That is the answer.
graph{- x - 2 [-10, 10, -5, 5]}
graph{- 3x + 2 [-10, 10, -5, 5]}