1990 AIME Problems/Problem 15

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Problem

Find $a_{}^{}x^5 + b_{}y^5$ if the real numbers $a_{}^{}$, $b_{}^{}$, $x_{}^{}$, and $y_{}^{}$ satisfy the equations

$ax + by = 3^{}_{},$
$ax^2 + by^2 = 7^{}_{},$
$ax^3 + by^3 = 16^{}_{},$
$ax^4 + by^4 = 42^{}_{}.$

Solution

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