Question

Given the inequalities y > 5x-8 and y >3x+4, find the point that satisfies neither inequalities

Answer 1

`\begin{cases}y>5x-8\\y>3x+4\end{cases}`
5x-8=3x+4
5x-3x=4+8
2x=12|:2
x=6
y=5x-8=5*6-8=30-8=22

`\begin{cases}x=6\\y=22\end{cases}`
For this point (6,22), both functions satisfy the inequality (intersect).

Shaded field points that also satisfy the inequality.

Answer 2

There might be many points that satisfy neither inequalities..