Question

Solve graphically : $3x+2y\ge 0$

Answer 1

Consider the line whose equation is $3x+2y=0$. The constant term is zero, therefore this line is passing through the origin.
$\therefore$one point on the line is O = (0, 0).
To find the another point, we can give any value of x and get the corresponding value of y.
Put $x=2,$ we get $6+2y=0i.e.y=-3$
$\therefore A=(2,-3),$is another point on the line. Draw theline OA.
To find the solution set, we cannot check (0, 0) as it is already on the line.
We can check any other point which is not on the line.
Let us check the point (1, 1).
When $x=1,y=1,then3x+2y=3+2=5$ which is greater than zero.
$\therefore 3x+2y>0$ in this case.
Hence (1, 1) lies in the required region.
Therefore, the required region is the upper side which is shaded in the graph.
This is the solution set of $x+2y>0.$