Question

How do you graph the system of linear inequalities `5x-3y<=4` and `x+y<8` and `y>3`?

Answer 1

f1(x,y) = 5x - 3y - 4 <= 0
f2(x,y) = x + y - 8 < 0
f3(y) = y - 8 > 0
This system of linear inequalities in 2 variables must be solved by graphing.
First, graph the 2 lines f1(x,y) and f2(x,y) by axis intersects.
f1(x,y) = 5x - 3y - 4 = 0
x = 0 --> `y = - 4/3`
y = 0 --> `x = 4/5`
f2(x,y) = x + y - 8 = 0
x = 0 --> y = 8
y = 0 --> x = 8
The solution set of `f(1(x,y) <= 0` is the area below the line f1(x,y)
The solution of f2(x,y) < 0 is the area below the line f2(x,y)
The solution set of f3(x,y) > 3 is the area above the line y = 3.
The solution set of the system is the commonly shared area of the 3 above solutions sets.