Question

Represent to solution set of each of the following in equations graphically in two dimensional plane :
$x\le 8-4y$

Answer 1

We have,

$x\le 8-4y$

Converting the inequation into equation,we obtain,x=8-4y

Putting y=0, we get x=8

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

So,this line meets x-axis at (8,0) and y-axis at (0,2).

we plot these points and join them by a thick 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 inequation (i),we get,$0\le 8$

Clearly,(0,0) satisfies the inequality.So,the region containing the origin is represented by the given inequation as shown below: