Which of the following ordered pairs is part of the solution set for the equation y = 5x2 - 2?
• (-1,43)
• (1,5)
• (-1,3)
• (-1,5)
To determine if an ordered pair is a solution to the equation, we substitute the x-coordinate into the equation and see if the resulting y-coordinate matches the given value.
Let's check each ordered pair one by one:
1. (-1, 43):
Plugging x = -1 into the equation y = 5x^2 - 2:
y = 5(-1)^2 - 2 = 5 - 2 = 3
The y-coordinate, 3, does not match the given value of 43. So, (-1, 43) is not a solution to the equation.
2. (1, 5):
Plugging x = 1 into the equation y = 5x^2 - 2:
y = 5(1)^2 - 2 = 5 - 2 = 3
The y-coordinate, 3, does not match the given value of 5. So, (1, 5) is not a solution to the equation.
3. (-1, 3):
Plugging x = -1 into the equation y = 5x^2 - 2:
y = 5(-1)^2 - 2 = 5 - 2 = 3
The y-coordinate, 3, matches the given value of 3. So, (-1, 3) is a solution to the equation.
4. (-1, 5):
Plugging x = -1 into the equation y = 5x^2 - 2:
y = 5(-1)^2 - 2 = 5 - 2 = 3
The y-coordinate, 3, does not match the given value of 5. So, (-1, 5) is not a solution to the equation.
Therefore, the ordered pair (-1, 3) is the only solution to the equation y = 5x^2 - 2.