Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ Question 4: Solve the given inequality graphically in two-dimensional plane: Solution 4: The graphical representation of y82x y82x is given in the figure below. This line divides the xy-plane in two half planes. Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 0 8 2 0 or 8 0 , which is true Therefore, lower half plane is not the solution region of the given inequality. Also, it is evident that any point on the line satisfies the given inequality. Thus, the solution region of the given inequality is the half plane containing the point (0, 0) including the line. The solution region is represented by the shaded region as follows. Question 5: Solve the given inequality graphically in two-dimensional plane: Solution 5: The graphical representation of x y 2 is given in the figure below. x y2 This line divides the xy-plane in two half planes. Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 6 – Linear Inequalities Maths ______________________________________________________________________________ We select the point as (0, 0). It is observed that, 0 0 2 or 0 2, which is true Therefore, the lower half plane is not the solution region of the given inequality. Also, it is clear that any point on the line satisfies the given inequality. Thus, the solution region of the given inequality is the half plane containing the point (0, 0) including the line. The solution region is represented by the shaded region as follows. Question 6: Solve the given inequality graphically in two-dimensional plane: 2 3 6 Solution 6: The graphical representation of 2 3 6 x y x y is given as dotted line in the figure below. This line divides the xy-plane in two half planes. Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not. We select the point as (0, 0). It is observed that, 2 0 3 0 6 or 0 6, which is false Therefore, the upper half plane is not the solution region of the given inequality. Also, it is clear that any point on the line does not satisfy the given inequality. Thus, the solution region of the given inequality is the half plane that does not contain the point (0, 0) including the line. The solution region is represented by the shaded region as follows. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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Class XI Chapter 13 - Limits and De

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