To determine which ordered pair is a solution to the equation \( y = 5x^2 - 2 \), we can substitute the \( x \) value from each ordered pair into the equation and see if it gives the corresponding \( y \) value.
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For the pair (1, 5): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not equal 5, so (1, 5) is not a solution.
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For the pair (-1, 43): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not equal 43, so (-1, 43) is not a solution.
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For the pair (-1, 5): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not equal 5, so (-1, 5) is not a solution.
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For the pair (-1, 3): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This equals 3, so (-1, 3) is a solution.
The only ordered pair that is a solution to the equation \( y = 5x^2 - 2 \) is (-1, 3).