To determine which of the ordered pairs is part of the solution set for the equation \( y = 5x^2 - 2 \), we need to substitute the x-value from each ordered pair into the equation and see if the resulting y-value matches the y-value in the ordered pair.
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For the pair \((-1, 43)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \(43\).
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For the pair \((-1, 5)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \(5\).
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For the pair \((1, 5)\): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match \(5\).
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For the pair \((-1, 3)\): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches \(3\).
From this analysis, the ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is \((-1, 3)\).