Question

The graphical solution of $-3x+2y\ge -6$ is represented by shade the

• A. half plane II including the points on the line $-3x+2y=-6$
• B. half plane II excluding the points on the line $-3x+2y=-6$
• C. half plane l including the points on the line $-3x+2y=-6$
• D. half plane l excluding the points on the line $-3x+2y=-6$

Answer 1

Answer: (C)

The given inequation is $-3x+2y\ge -6$...(i)
Step I Consider the inequation as a strict equation
i.e., $-3x+2y=-6$
Step II Find the points on the $X$-axis and $Y$-axis i.e.,

Step III Plot the graph using the above table.
Step IV Take a point $(0,0)$ and put it in the given inequation (i), we get $0+0\ge -6$
which is true, so the shaded region will be towards the origin.
Hence, the shaded half plane I including the points on the line is the solution of given inequality.