91Ó°ÊÓ

The system of inequality is$\left\{\begin{array}{l}x-y>-1\\ y<\frac{1}{3}x-2\end{array}\right.$

To find the solution of inequality by graphing

Graph the line$x-y=-1$

It is a dashed line since it contains the inequality $>$.

And test the point $(0,0)$.

It is a solution to the given inequality, so shade the region that contains the point$(0,0)$

Graph the line $y=\frac{1}{3}x-2$

with slope $m=\frac{1}{3}$and $y-$intercept $-2$

The boundary line is dashed line since it contains the inequality $<$.

Test the inequality with point $(0,0)$

It is not a solution so shade the region that does not contain the point $(0,0)$.

The point where the boundary line intersect is not a solution since it is not a solution to both the inequalities.

The solution is all the points in the area shaded twice which appears as the darkest shaded region.

Choose $(0,-3)$as a test point

Test for first inequality:

$x-y>-1$

$0-(-3)>-1$

$3>-1$is true.

Test for second inequality:

$y<\frac{1}{3}x-2$

$-3<\frac{1}{3}\left(0\right)-2$

$-3<-2$is true.

The region containing $(0,-3)$is the solution to the system.