Answer:
See explanation
Step-by-step explanation:
Plot the solution sets to both inequalities.
1. For the inequality [tex]y<2x+5.[/tex] First, plot the dotted line [tex]y=2x+5[/tex] (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.
[tex]2\cdot 0-5=-5<0[/tex]
so the origin does not belong to the needed part. Shade the part, which does not include origin.
2. For the inequality [tex]y>-3x+1.[/tex] First, plot the dotted line [tex]y=-3x+1[/tex] (dotted because sign is without notion "or equal to"), then choose correct part by substitution coordinates of the origin.
[tex]-3\cdot 0+1=1>0[/tex]
so the origin does not belong to the needed part. Shade the part, which does not include origin.
3. Find the common region of these two shaded parts - this is the solution to the system of two inequalities.
