how can you tell that a system of inequalities does not have a solution?

Question

please help i also need an example

Answer 1

1. y₁ ≥ m₁x + b₁  ...... (1)
    y₂ ≤ m₂x + b₂  ...... (2)
if m₁ = m₂ and b₁ ≠ b₂ , lines are parallel and shading areas (for (1) is above the line and for (2) under the line) do not overlap, system does not have a solution.
2. A₁ x + B₁ y ≥ C₁
    A₂ x + B₂ y ≤ C₂
First solve each inequality for y .

y ≥ x +5              y > -4x + 8  
y < x - 4              y ≤ -4x + 4