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 it not satisfies the inequality than the shaded region is opposite to the point.

The two inequalities are$y≤x+4$and $2y≤x-3.$

The linear equation of the respective inequalities are $y=x+4$and $2y=x-3.$

Points which satisfy the equation $y=x+4$are $\left(0,4\right)$and$\left(-4,0\right)$.

Points which satisfy the equation $2y=x-3$are $\left(3,0\right)$and $\left(1,-1\right)$.

We choose the point$\left(0,0\right)$.

The point$\left(0,0\right)$satisfy both the inequalities $y-4≤x≤2y+3.$

So, the graph of the inequality is

The common region is $y-4≤x≤2y+3.$