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Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Solve the given inequality in two-dimensional plane . $x+y < 5$

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Toolbox:
  • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
  • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
  • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .
  • 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 $ x+y < 5$ consider the equation .
$x+y <5$
$(5,0) $ and $(0,5)$ satisfy the equation
The line $x+y =5$ is represented as a dotted line in the graph.
The line divides the plane into two half planes I and II.
Select a point not an line say (0,0)
Step 2:
We observe that , $0+0 <5$
$ 0 < 5$
Which is true (0,0) satisfies the given inequality
$\therefore $ half plane II is not the solution region.
Step 3:
The solution region of the given inequality is the shaded half plane I. not including the line.
answered Jul 28, 2014 by meena.p
 
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