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Q.
The solution set of the inequalities $2 x+y \geq 4$, $x+y \leq 3,2 x-3 y \leq 6$ is
Linear Inequalities
Solution:
The given system of inequalities
$2 x+y \geq 4$...(i)
$x+y \leq 3 $...(ii)
$2 x-3 y \leq 6$...(iii)
Step I Consider the inequations as strict equations
i.e. $2 x+y=4$
$x+y=3$
$2 x-3 y=6$
Step II Find the points on the $X$-axis and $Y$-axis for,
$2 x+y=4$
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
$0+0 \geq 4$(false)
So, the shaded region will be away from origin.
$0+0 \leq 3$(true)
So, the shaded region will be towards origin.
$0-0 \leq 6$(true)
So, the shaded region will be towards origin.
Thus, common shaded region shows the solution of the inequalities.
