To answer this question let's look at each line first.
The slant line can be express by the equation:
[tex]y=x[/tex]We notice that the shaded part is above this line, then we have that that inequality is written as:
[tex]y\ge x[/tex]Now, the horizontal line is express as:
[tex]y=1[/tex]since the shaded region is below that line and the line is dashed the inequality is:
[tex]y<1[/tex]Therefore, the system of inequalities is:
[tex]\begin{gathered} y\ge x \\ y<1 \end{gathered}[/tex]