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Solve the given inequality in two - dimensional plane $y+8 \geq 2x$

$\begin{array}{1 1} 1 \\ 0 \\ equal \\ not\; equal \end{array} $

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  • 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
$y+8 \geq 2x$
Consider the equation $y+8 =2x$
We see that $(4,0)$ and $(0,-8)$ Satisfy the given equation .
The graphical representation of the line $y+8=2x$ is given below
Step 2 :
The line divides the XY plane into two region I and II select a point not on the line say (0,0) in the half plane I , We see that
$0+8 \geq 2(0)$
$8 \geq 0$ is true.
$\therefore $ The half plane II is not a solution region of the given inequality .
Step 3:
The Solution region of the given inequality is the half plane I containing (0,0) including the points on the line .
answered Jul 30, 2014 by meena.p
edited Jul 30, 2014 by meena.p
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