Which ordered pair is in the solution set of the system of equations shown below? Y^2-x^2+32=0 and 3y-x=0. A. (2,6) B. (3,1) C. (-1,-3) D. (-6,-2)

The ordered pair (-6, -2) is in the solution set of the system of equations shown below ⇒ D

Step-by-step explanation:

To find the ordered pair that is in the solution set of the system of the equation substitute x and y in each equation by the coordinates of the ordered pair, if the two sides of equations are equal, then the ordered pair is in the solution set of the system of equations

∵ The equations are y² - x² + 32 = 0 ⇒ (1) and 3y - x = 0 ⇒ (2)

∵ The 1st ordered pair is (2, 6)

∴ x = 2 and y = 6

→ Substitute them in equation (2) first

∵ The left side = 3y - x

∴ The left side = 3(6) - 2 = 18 - 2 = 16

∵ The right sides = 0

∴ Left side ≠ Right side

∴ (2, 6) is not a solution to the system of equations

∵ The 2nd ordered pair is (3, 1)

∴ x = 3 and y = 1

→ Substitute them in equation (2) first

∵ The left side = 3y - x

∴ The left side = 3(1) - 3 = 3 - 3 = 0

∵ The right sides = 0

∴ Left side = Right side

→ Substitute them in equation (1)

∵ The left side = y² - x² + 32

∴ The left side = (1)² - (3)² + 32 = 1 - 9 + 32 = 24

∵ The right sides = 0

∴ Left side ≠ Right side

∴ (3, 1) is not a solution to the system of equations

∵ The 3rd ordered pair is (-1, -3)

∴ x = -1 and y = -3

→ Substitute them in equation (2) first

∵ The left side = 3y - x

∴ The left side = 3(-3) - (-1) = -9 + 1 = -8

∵ The right sides = 0

∴ Left side ≠ Right side

∴ (-1, -3) is not a solution to the system of equations

∵ The 4th ordered pair is (-6, -2)

∴ x = -6 and y = -2

→ Substitute them in equation (2) first

∵ The left side = 3y - x

∴ The left side = 3(-2) - (-6) = -6 + 6 = 0

∵ The right sides = 0

∴ Left side = Right side

→ Substitute them in equation (1)

∵ The left side = y² - x² + 32

∴ The left side = (-2)² - (-6)² + 32 = 4 - 36 + 32 = 0

∵ The right sides = 0

∴ Left side = Right side

∴ (-6, -2) is a solution to the system of equations

The ordered pair (-6, -2) is in the solution set of the system of equations shown below

4x and 6y

im not sure though

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.