Answer:
Purple region of the attached graph.
Step-by-step explanation:
First, we are replacing the inequality symbol (<) by an equality symbol (=) and solve for [tex]y[/tex] to find the line boundaries of each inequality:
For [tex]2x+5y<10[/tex]
[tex]2x+5y=10[/tex]
[tex]5y=-2x+10[/tex]
[tex]y=-\frac{2}{5} y+\frac{10}{5}[/tex]
[tex]y=-\frac{2}{5} y+2[/tex]
For [tex]x-y<5[/tex]
[tex]x-y=5[/tex]
[tex]-y=-x+5[/tex]
[tex]y=x-5[/tex]
Now, since both inequalities have the symbol (<), the lines [tex]y=-\frac{2}{5} y+2[/tex] and [tex]y=x-5[/tex] are dotted lines. The solution of the system of inequalities is the shaded region bounded by the two lines. Notice that since the line are dotted, no solution of the inequality lie in any of the lines themselves.
