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Find the linear inequalities for which the shaded region in the given figure is the solution set

Answers (1)

Let us consider,

x + y = 8,

Now, from the graph we can say that the constraint x+y\leq 8 is satisfiedsince the shaded region and the origin are on the same side of the line.

Now, let us consider, x + y = 4,

Here, the constraint x+y\geq 0 is not satisfied since the origin is on the opposite side of the shaded region.

Thus, the required constraint is x+y\geq 4

Now, we know that,

Shaded region in the first quadrant is x\geq 0 &y\geq 0

& shaded region below the line y = 5 & left to the line x = 5 is

y\leq 0   & x\geq 0

Therefore, the linear inequalities are,

x+y\leq 8

x+y\geq 4

x\geq 0

&y\geq 0

x\leq 5y\leq 5

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