From the problem, we have the inequalities :
![\begin{gathered} x+2y<6 \\ yNote that the boundary line is <strong>dashed</strong> if the symbols are < or >.<p></p><p>Let's graph first the first inequality :</p>[tex]\begin{gathered} x+2y<6 \\ \text{Change the symbol into ''=''} \\ x+2y=6 \\ \text{Solve for the intercepts} \\ \text{when x = 0} \\ 0+2y=6 \\ y=(6)/(2)=3 \\ \\ \text{when y = 0} \\ x+2(0)=6 \\ x=6 \end{gathered}]()
Plot the points (0, 3) and (6, 0)
The region will pass through the origin if (0, 0) satisfies the inequality.
Test for (0, 0)
Since it is true, the region will pass through the origin.
The graph will be :
Next is to graph the second inequality :
[tex]\begin{gathered} yPlot the points (0, -5) and (5, 0)
Check again origin (0, 0) to the inequality :
[tex]\begin{gathered} ySince it is false, the region will not pass through the origin.
Tha graph will be :
The solution to the system is the overlapping region between the two inequalities.