91Ó°ÊÓ

The solution of linear inequalities can be obtained by changing the inequalities into equations and solving the linear equations to obtain a graph. Then the common shaded region is a solution of the inequalities.

The shaded region obtained by choosing a point, if the point satisfies the inequality the region is along the point, if not satisfies the inequalities, then the shaded region is opposite to the point.

The given inequalities are-:

$\begin{array}{c}yâ‰\yen x-3\\ yâ‰\yen -x+1\end{array}$

The linear equation of the inequalities is-:

$\begin{array}{c}y=x-3\\ y=-x+1\end{array}$

The point which satisfies the equation $y=x-3$ are $(0,-3)$and$(3,0)$.

The point which satisfies the equation $y=-x+1$ are $(0,1)$ and$(1,0)$.

We choose $(0,0)$then the point $(0,0)$ satisfies the inequality $yâ‰\yen x-3$ but it does not satisfy the inequality $yâ‰\yen -x+1$.

So, the graph of the inequality is

The common region is$-y+1≤x≤y+3$