To determine which ordered pairs are part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the x-value from each ordered pair into the equation and see if it produces the corresponding y-value.
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For the pair (1, 5):
- Substitute \( x = 1 \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
- The y-value is 3, not 5. So, (1, 5) is not a solution.
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For the pair (-1, 43):
- Substitute \( x = -1 \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
- The y-value is 3, not 43. So, (-1, 43) is not a solution.
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For the pair (-1, 3):
- Substitute \( x = -1 \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
- The y-value is 3, which matches the pair (-1, 3). So, (-1, 3) is a solution.
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For the pair (-1, 5):
- Substitute \( x = -1 \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \]
- The y-value is 3, not 5. So, (-1, 5) is not a solution.
The only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is C. (-1, 3).