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Q.
The graphical solution of the inequalities $x+2 y \leq 10, x+y \geq 1, x-y \leq 0, x \geq 0, y \geq 0$ is
Linear Inequalities
Solution:
The given system of inequalities
$x+2 y \leq 10 $...(i)
$x+y \geq 1$...(ii)
$x-y \leq 0 $ ...(iii)
$x \geq 0, y \geq 0$...(iv)
Step I Consider the given inequations as strict equations i.e.,
$x+2 y =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 $x+2 y=10$, $x+y=1, x-y=0$ using the above tables.
Step IV Take a point $(0,0)$ and put it in the inequations (i) and (ii),
$0+0 \leq 10 \text { (true) }$
So, the shaded region will be towards origin.
And $ 0+0 \geq 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
$2 \geq 0,2 \geq 0$ (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
$0-1 \leq 0 \text { (true) }$
So, the shaded region will be towards point $(0,1)$.
Thus, common shaded region shows the solution of the inequalities.
