To find which ordered pairs are part of the solution set for the equation \( y = 5x^2 - 2 \), we can substitute the x-values from each ordered pair into the equation and see if we get the corresponding y-values.
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For the pair (1, 5): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This gives us \( (1, 3) \neq (1, 5) \). So this pair is not a solution.
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For the pair (-1, 5): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This gives us \( (-1, 3) \neq (-1, 5) \). So this pair is not a solution.
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For the pair (-1, 3): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This gives us \( (-1, 3) = (-1, 3) \). So this pair is a solution.
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For the pair (-1, 43): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This gives us \( (-1, 3) \neq (-1, 43) \). So this pair is not a solution.
Thus, the only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is:
C. (-1, 3).