Question

Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system.

Answer 1

Given:

The system of inequalities:

$x>3$

$y$

To find:

The point that represents a solution to the system by using the graph.

Solution:

We have,

$x>3$

$y$

The related equations of these inequalities are:

$x=3$

$y=2x-5$

The line $x=3$ is a vertical line that intersect the x-axis at 3.

The table of values for $y=2x-5$ is:

x         y

0       -5

1        -3

Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.

The boundary lines are dotted lines because the points on the lines are not included in the solution set.

Check the inequalities for (0,0).

First inequality: $0>3$           ( False)

Second inequality: $0$

                               $0$     (False)

Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).

Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.

From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.

Therefore, the correct option is C.