Question

The graphical solution of the inequalities $x+2y\le 10,x+y\ge 1,x-y\le 0,x\ge 0,y\ge 0$ is

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

The given system of inequalities
$x+2y\le 10$...(i)
$x+y\ge 1$...(ii)
$x-y\le 0$ ...(iii)
$x\ge 0,y\ge 0$...(iv)
Step I Consider the given inequations as strict equations i.e.,
$x+2y=10,x+y=1,x-y=0$
and $x=0,y=0$
Step II Find the points on the $X$-axis and $Y$-axis for

Step III Plot the graph of $x+2y=10$, $x+y=1,x-y=0$ using the above tables.
Step IV Take a point $(0,0)$ and put it in the inequations (i) and (ii),
$0+0\le 10\text{ (true) }$
So, the shaded region will be towards origin.
And $0+0\ge 1$ (false)
So, the shaded region will be away from the origin.
Again, take a point $(2,2)$ and put it in the inequation (iv), we get
$2\ge 0,2\ge 0$ (true)
So, the shaded region will be towards point $(2,2)$.
And take a point $(0,1)$ and put it in the inequation (iii), we get
$0-1\le 0\text{ (true) }$
So, the shaded region will be towards point $(0,1)$.

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