Question

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$3x-2y\le x+y-8$

Answer 1

We have,

$3x-2y\le x+y-83x-2y\le x+y-8\Rightarrow 3x-x\le y+2y-8\Rightarrow 2x\le 3y-8...\left(i\right)$

Converting the inequation into equation,we obtain,2x=3y-8.

Putting y=0, we get x=$\frac{-8}{2}=-4$

Putting x=0, we get y=$\frac{8}{3}$

So, this line meets x-axis at (-4,0) and y-axis at $(0,\frac{8}{3})$.

we plot these points and join them by a line. This line divides the xy-plan in two parts. To determine the region represented by the given inequality consider the point 0(0,0).

Putting x=0,and y=0 in the in equation (i),we get,$0\le -8$

$\therefore$ We find that the point (0,0) does not satisfy the inequation $2x\le 3y-8$.So, the region represented by the given in equation is shown shaded region.