Question

Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21? Select each correct answer.

A) (7, 0)
B) (11, 3)
C) (−3, 3)
D) (−1, −6)

Answer 1

The ordered pairs that are solutions to the equation 3x - 4y = 21 are A) (7, 0), B) (11, 3), and D) (-1, -6) as their substitution in the equation produces a true statement.

Step-by-step explanation:

To determine which ordered pairs in the form (x, y) are solutions to the equation 3x - 4y = 21, we need to substitute the x and y values from each ordered pair into the equation and check if the equation holds true.

1. (7, 0): Substitute x = 7 and y = 0 into the equation.
   3(7) - 4(0) = 21
   21 = 21 (True, so this is a solution)
2. (11, 3): Substitute x = 11 and y = 3 into the equation.
   3(11) - 4(3) = 33 - 12 = 21 (True, so this is also a solution)
3. (-3, 3): Substitute x = -3 and y = 3 into the equation.
   3(-3) - 4(3) = -9 - 12 = -21 (False, so this is not a solution)
4. (-1, -6): Substitute x = -1 and y = -6 into the equation.
   3(-1) - 4(-6) = -3 + 24 = 21 (True, so this is a solution)

The correct answers are: A) (7, 0), B) (11, 3), and D) (-1, -6).