Question

The graph below shows the solution to which system of inequalities?

Answer 1

Given:

The graph of system of inequalities.

To find:

The inequalities.

Solution:

From the given graph it is clear that dotted line is a vertical line parallel to the x-axis and one unit above the x-axis. So, the equation of dotted line is

$y=1$

The area below the dotted line is shaded. It means, y values must be less than 1. So, the required inequality for dotted line is

$y<1$         ...(i)

Solid line passes through (-5,-5), (0,0) and (5,5). It means y is directly proportional to x with 1 as constant of proportionality. So, the equation of solid line is

$y=x$

The area above the solid line is shaded. It means, y values must be greater than or equal to x. So, the required inequality for solid line is

$y\geq x$      ...(ii)

So, the system of inequalities have inequalities $y<1$ and $y\geq x$.

Therefore, the correct option is D.