Question

This graph shows the solutions to the inequalities y > x-2 and y< x-10.Does the system of inequalities have solutions? If so, which region containsthe solutions?

Answer 1

We are given the solution graph of the following inequation system:

$\begin{gathered} y>\frac{3}{2}x-2 \\ y<\frac{3}{2}x-10 \end{gathered}$

We need to have into account that a system of inequalities has a solution where the graph of their solutions intercepts. If the graph does not intercept then there is no solution. In the given case, the graph of both inequalities do not intercept, therefore there is no solution.