Determine which ordered pair is a solution of y = x2–2.
(5, 21), (–5, 24), (–1, –1), (–2, 6)
A. (–2, 6)
B. (5, 21)
C. (–1, –1)
D. (–5, 24)
C. (–1, –1)
To determine which ordered pair is a solution of y = x^2 - 2, we substitute the x-value of each ordered pair into the equation and see if the resulting y-value matches.
Let's go through each ordered pair:
1. Ordered pair (5, 21):
- Substituting x = 5 into the equation, we get y = 5^2 - 2 = 25 - 2 = 23.
- Since the resulting y-value (23) does not match the given y-value (21), this ordered pair is not a solution.
2. Ordered pair (-5, 24):
- Substituting x = -5 into the equation, we get y = (-5)^2 - 2 = 25 - 2 = 23.
- Since the resulting y-value (23) does not match the given y-value (24), this ordered pair is not a solution.
3. Ordered pair (-1, -1):
- Substituting x = -1 into the equation, we get y = (-1)^2 - 2 = 1 - 2 = -1.
- The resulting y-value (-1) matches the given y-value (-1), so this ordered pair is a solution.
4. Ordered pair (-2, 6):
- Substituting x = -2 into the equation, we get y = (-2)^2 - 2 = 4 - 2 = 2.
- Since the resulting y-value (2) does not match the given y-value (6), this ordered pair is not a solution.
Therefore, the ordered pair that is a solution of y = x^2 - 2 is (–1, –1). So the answer is C. (–1, –1).
To determine which ordered pair is a solution of the equation y = x^2 - 2, you need to substitute the x and y values into the equation and check if the equation holds true.
Let's check each option:
A. (-2, 6):
Substituting x = -2 and y = 6 into the equation:
6 = (-2)^2 - 2
6 = 4 - 2
6 = 2
The equation is not true for this option, so (A) is not a solution.
B. (5, 21):
Substituting x = 5 and y = 21 into the equation:
21 = (5)^2 - 2
21 = 25 - 2
21 = 23
The equation is not true for this option, so (B) is not a solution.
C. (-1, -1):
Substituting x = -1 and y = -1 into the equation:
-1 = (-1)^2 - 2
-1 = 1 - 2
-1 = -1
The equation is true for this option, so (C) is a solution.
D. (-5, 24):
Substituting x = -5 and y = 24 into the equation:
24 = (-5)^2 - 2
24 = 25 - 2
24 = 23
The equation is not true for this option, so (D) is not a solution.
Therefore, the ordered pair that is a solution of y = x^2 - 2 is (C) (-1, -1).