Question

The solution set of the inequalities $2x+y\ge 4$, $x+y\le 3,2x-3y\le 6$ is

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

The given system of inequalities
$2x+y\ge 4$...(i)
$x+y\le 3$...(ii)
$2x-3y\le 6$...(iii)
Step I Consider the inequations as strict equations
i.e. $2x+y=4$
$x+y=3$
$2x-3y=6$
Step II Find the points on the $X$-axis and $Y$-axis for,
$2x+y=4$

Step III Plot the graph using the above tables.
Step IV Take a point $(0,0)$ and put it in the inequations (i), (ii), and (iii), we get
$0+0\ge 4$(false)
So, the shaded region will be away from origin.
$0+0\le 3$(true)
So, the shaded region will be towards origin.
$0-0\le 6$(true)
So, the shaded region will be towards origin.

Thus, common shaded region shows the solution of the inequalities.