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in Linear Equations by (15.7k points)

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

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1 Answer

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by (15.2k points)

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

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

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

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

Also , the region lies in the first quadrent Therefore x \(\ge\) 0 and y \(\ge\)0

Thus the linear inequation comprising the given solution set are +4y \(\le\)12, 4x + 3y \(\le\) 12, x \(\ge\) 0, y \(\ge\)0

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