Which points are solutions to the system of inequalities shown below? Check
all that apply
y< x
y> 5
x>2
A.(-3,8)
B.(7,5)
C.(8,6)
D.(9,7)
E.(6,6)
F.(3,2)

The points (8 ,6) and (9 , 7) are solutions of the system of inequalities ⇒ C and D

Step-by-step explanation:

Let us study each inequality and find the right solutions

∵ x > 2

∴ The x-coordinates of the points are 3, 6, 7, 8, 9

- That means answer A is out because its x-coordinate not greater

  than 2 ⇒ (-3 , 8)

∵ y > 5

∴ The y-coordinates of the points are 6, 7, 8

- That means answers B and F are out because y-coordinates

   of them not greater than 5 ⇒ (7 , 5) , (3 , 2)

∵ y < x

∴ The x-coordinate of the point is greater than the y-coordinate

- That means answer E is out because its x-coordinate is equal to

   the y-coordinate ⇒ (6 , 6)

∴ The points are (8 , 6) and (9 , 7) because their x-coordinates

   are greater than 2, their y-coordinates are greater than 5 and

    their y-coordinates are less than their x-coordinates

The points (8 ,6) and (9 , 7) are solutions of the system of inequalities

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.