logo

Ask Questions, Get Answers

X
 
Home  >>  CBSE XI  >>  Math  >>  Linear Inequalities

Solve the given inequality graphically in two -dimensional plane. $-3x+2y \geq -6$

1 Answer

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 $ -3x +2y \geq -6$
Consider the equation $-3x +2y =-6$
We see that $(2,0) $ and $(0,-3)$ satisfy the equation.
The graphical representation of the line is given below,
Step 2:
The line divides the xy plane into two half planes I and II
Consider a point (0,0) in the half plane I.
We see that , $-3 (0) +2(0) \geq -6$
$ 0 \geq -6$ is true.
Therefore the half plane II is not the solution region.
Step 3:
Thus the solution region of the given inequality is the half plane I containing the point (0,0) including the points on the line.
It is represented by the shaded region.
answered Jul 30, 2014 by meena.p
 
Download clay6 mobile appDownload clay6 mobile app
...
X