A pod of dolphins follows a conic path to their desired food source and then swims back into the deep water of the gulf. Some scientists track a specific pod and find their path to be described by the equation 5y2−6x2=−51.\displaystyle {5}{y}^{{2}}-{6}{x}^{{2}}=-{51}. At the same time, the scientists track a second pod of dolphins, whose path is described by the equation 2x2−y2=23.\displaystyle {2}{x}^{{2}}-{y}^{{2}}={23}. At which point in the first quadrant will the two pods meet?

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