Find the linear inequalities for which the shaded area is the solution set in the figure given below.

We have seen that the shaded region and origin are on the same side of the line $3 x+4 y=12$

For $(0,0)$ we have $0+0-12<0$. So the shaded region satisfies the inequality $3 x+4 y \leq 12$.

We have seen that the shaded region and origin are on the same side of the line $4 x+3 y=12$

For $(0,0)$ we have $0+0-12<0$. So the shaded region satisfies the inequality $4 x+3 y \leq 12$.

Also, the region lies in the first quadrent. Therefore $x \geq 0$

and $y \geq 0$

Thus the linear inequation comprising the given solution set are $+4 y \leq 12,4 x+3 y \leq 12, x \geq 0, y \geq 0$