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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Q)

Solve the given inequality graphically in two - dimensional plane . $ y < -2$

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A)
Toolbox:
  • To represent the solution of linear inequality of one or two variable in a plane if the inequality involves $'\geq'$ or $' \leq$ we draw the graph of the line as a thick line to indicate the line is included in the solution set.
  • If the inequality involves $'>'$ as $'<'$ we draw the graph of the line using is not included in the solution set.
  • To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
  • We consider the corresponding equation $ax+by =c$ which represents a straight line This line divides the plane into two half planes I and II
  • We take any point in I half plane and check if it satisfies the given inequality will be one half plane (called solution region ) Containing the point satisfying the inequality
The given inequality is $y <-2$
Consider the equation $y=-2$
The graph of the dotted line $y=-2$ is given below.
<< Enter Text >>
Step 2:
The line $y=-2$ divides the XY- Plane into two half planes I and II
We select a point not on the line (0,0) in the half plane I.
We see that $0 < -2$ is false
Step 3:
Thus the half plane I containing the point (0,0) is not the solution region.
The solution region of the given inequality is the half plane II not containing the line .
It is represented by the shaded region.
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