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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblema 35
Capitolo 6, Problema 35

In Exercises 29–42, solve each system by the method of your choice. {x3+y=0x2−y=0\(\begin{cases}\) x^3 + y = 0 \\ x^2 - y = 0 \(\end{cases}\)

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Start with the given system of equations: \(x^3 + y = 0\) and \(x^2 - y = 0\).
From the second equation, express \(y\) in terms of \(x\): \(y = x^2\).
Substitute \(y = x^2\) into the first equation to eliminate \(y\): \(x^3 + x^2 = 0\).
Factor the resulting equation: \(x^2(x + 1) = 0\).
Set each factor equal to zero and solve for \(x\): \(x^2 = 0\) or \(x + 1 = 0\), then find corresponding \(y\) values using \(y = x^2\).

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