91Ó°ÊÓ

We have to find the solution to the given system by using graphing

For inequality y<3x+1, first, we graph the line y=3x+1 and then draw a boundary line. we can see that at (0,0) inequality is true, where we have to shade .

Then the graph is given below

We graph the inequality on the same graph. Here to make graph the line $y=-x-2$and then draw the boundary line for inequality, since testing at(0,0) made inequality true and shade this region

Then the graph is given below

Here the solution is the region where the shading overlaps.

We can take (1,-2) as a checking point

$$\begin{gathered} \mathrm{Put}\mathrm{x}=1\mathrm{and}\mathrm{y}=-2\mathrm{in}\mathrm{y}<3\mathrm{x}+1 \\ -2<3×1-2 \\ -2<1\mathrm{true} \\ \mathrm{Ordered}\mathrm{pair}(-2,1)\mathrm{is}\mathrm{true}\mathrm{for}\mathrm{this}\mathrm{inequality} \\ \mathrm{Substitue}\mathrm{x}=1\mathrm{and}\mathrm{y}=-2\mathrm{in}\mathrm{y}â‰\yen -\mathrm{x}-2 \\ -2â‰\yen -1-3 \\ -2â‰\yen -4\mathrm{statement}\mathrm{is}\mathrm{true} \\ \mathrm{Thus}\mathrm{both}\mathrm{inequalities}\mathrm{is}\mathrm{true}\mathrm{for}(-2,1),\mathrm{hence}(-2,1)\mathrm{is}\mathrm{the}\mathrm{solution}. \end{gathered}$$