Question

1. \

$$\begin{cases} 2x + 5y > 20 \\\\ 2x + 5y < -5 \\end{cases}$$

Explanation:

Step1: Analyze the inequalities

Let \( z = 2x + 5y \). The system of inequalities is \(

$$\begin{cases}z>20\\z < - 5\end{cases}$$

\)

Step2: Check for solution existence

A number \( z \) cannot be simultaneously greater than 20 and less than - 5 because the set of numbers greater than 20 (\( (20,+\infty) \)) and the set of numbers less than - 5 (\( (-\infty,-5) \)) are disjoint. There is no real number \( z \) that satisfies both inequalities at the same time. So the system of inequalities has no solution.

Answer:

The system of inequalities \(

$$\begin{cases}2x + 5y>20\\2x + 5y < - 5\end{cases}$$

\) has no solution.