To determine which ordered pair is 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 the resulting \( y \) matches the given \( y \) value.
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For the pair \((-1, 43)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] So, \( (-1, 43) \) is not a solution.
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For the pair \((1, 5)\): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] So, \( (1, 5) \) is not a solution.
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For the pair \((-1, 5)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] So, \( (-1, 5) \) is not a solution.
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For the pair \((-1, 3)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] So, \( (-1, 3) \) is a solution.
The only ordered pair that fits the equation \( y = 5x^2 - 2 \) is \( (-1, 3) \).