We need to solve graphically the system of inequalities:
[tex]\begin{gathered} 2x+7y<14 \\ x\geq-3 \end{gathered}[/tex]
Part 1: Solution of the first linear inequality
The boundary line for the solution to the first inequality is:
[tex]\begin{gathered} 2x+7y=14 \\ \\ 7y=-2x+14 \\ \\ y=-\frac{2}{7}x+\frac{14}{7} \\ \\ y=-\frac{2}{7}x+2 \end{gathered}[/tex]
Thus, two points on the boundary line are (0,2) and (7,0) since:
[tex]\begin{gathered} x=0\Rightarrow y=2 \\ \\ x=7\Rightarrow y=-2+2=0 \end{gathered}[/tex]
Since the solution set corresponds to all points for which the y-coordinate is less than (not equal to) those of the points on the boundary line, this line is dashed.
And the solution region is all the points below that line:
Part 2: Solution of the second inequality
The boundary line for the second inequality is:
