Given:
The system of inequalities is:
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
To find:
The graph of the given system of inequalities.
Solution:
We have,
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
The related equations are:
[tex]y=-\dfrac{1}{3}x+1[/tex]
[tex]y=2x-3[/tex]
Table of values for the given equations is:
[tex]x[/tex] [tex]y=-\dfrac{1}{3}x+1[/tex] [tex]y=2x-3[/tex]
0 1 -3
3 0 3
Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].
Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].
The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.
Therefore, the graph of the given system of inequalities is shown below.
