Question

How do you solve this system of equations: `3x + 2y \leq - 1; x + 4y > - 12`?

Answer 1

This is a system of linear inequalities in 2 variables, in standard form:
`f(x) = 3x + 2y + 1 <= 0` (1)
`g(x) = x + 4y + 12 > 0` (2)
First, graph the Line 1 --> f(x ) = 0 by axis -intercepts:
x = 0 --> `y = -1/2`
y = 0 --> `x = - 1/3`
Next, graph the Line 2 --> g(x) = 0 by axis-intercepts
x = 0 --> y = - 3
y = 0 --> x = -12
The solution set of the inequality (1) is the area below the Line 1.
The solution set of the inequality (2) is the area above the Line 2.
The combined solution set is the area commonly shared by the 2 solution set areas. Color this area that shows the answer.
graph{3x + 2y + 1 = 0 [-5, 5, -2.5, 2.5]}
graph{x + 4y + 12 = 0 [-20, 20, -10, 10]}