Question

Which of the following is a solution to the following system of inequalities let the green region represents the answer region

x+2y< or equal to 4
3x-y> 2

Answer 1

The given inequalities are

x+2y≤4, 3x-y>2

To plot the graph first convert it into slope intercept form in two coordinate system i.e To convert equation of the type Ax + By= C in Slope intercept form

x/C÷A + y/C÷B =1

So,the equation becomes

x/4 + y/2≤ 1,

x/2÷3 + y/-2>1,

We have to also consider x>0 and y>0.

Now The shaded area in green is shown in the graph.

x=8/7 and y=20/7 is the point of intersection of lines

A triangular region is formed having vertices (0,0) (4,0) and (8/7,20/7) is the required solution.