Question

Solve the given inequalities graphically:

$3x+2y$ $\le$ $12,x$ $\ge$ $1,y$ $\ge$$2$

Answer 1

Draw the line $3x+2y=12,x=1$ and $y=2$. Now check for the position of origin w.r.t. the given lines to determine the solution of the inequalities.

For $3x+2y-12$ at $(0,0)$, $3\left(0\right)+2\left(0\right)-12<0$. Hence, $(0,0)$ lies in the inequality $3x+2y\le 12$

For $x-1$ at $(0,0)$, $0-1<0$. Hence, $(0,0)$ doesn't lie in the inequality $x\ge 1$

For $y-2$ at $(0,0)$, $0-2<0$. Hence, $(0,0)$ doesn't lie in the inequality $y\ge 2$.

The shaded part in the above graph represents the solution of the given inequlities.