91Ó°ÊÓ

To solve the inequalities we convert the inequalities into linear equations and find the solutions of the equations to obtain the graph.

For shading the region, we choose a point. If the point satisfies the inequalities then the shaded region is towards the point otherwise, the shaded region is away from the point.

Given inequalities are$3x-4≤y≤x+3.$

Their respective linear equations are$y=3x-4$ and$y=x+3.$

The points which satisfy the equation $y=3x-4$ are$(0,-4)$ and.$(1,-1)$

The points, which satisfy the equation$y=x+3$ are$(0,3)$ and$(-3,0).$

We choose$(0,0)$ to get the shaded region. The point $(0,0)$ satisfies both the inequalities .$yâ‰\yen 3x-4,y≤x+3$

Therefore, the graph for the inequalities is

The common shaded region is$3x-4≤y≤x+3.$