Question

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

x > 3 y < 2x - 5 answers: (-3, -1) (1, 11) (4, -1) (5, 6)

Answer 1

Given:

The system of inequalities:

`x>3`

`y<2x-5`

To find:

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

Solution:

We have,

`x>3`

`y<2x-5`

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<2(0)-5`

`0<-5` (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.