Browse Questions

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

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
Step 1:
The given inequality is $2x -3y >6$
Consider the equation $2x-3y=6$
We see taht the points $(3,0)$ and $(0,-2)$ satisfy the equation.
The graphical representation of the line is given below.
Step 2:
The line divides the XY -plane into two half- plane I and II .
Consider a point (0,0) in half plane I
We see that $2(0) -3(0) >6$
$0 > 6$ is false
The half plane I containing the point (0,0) is not the solution region of the inequality.
Step 3:
Thus the solution region of the given inequality is the half plane II excluding the line . It is represented by the shaded region.