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Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblema 49
Capitolo 6, Problema 49

In Exercises 47–52, solve each system by the method of your choice. {−4x+y=12y=x3+3x2\(\begin{cases}\) -4x + y = 12 \\ y = x^3 + 3x^2 \(\end{cases}\)

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Start with the given system of equations: \(-4x + y = 12\) and \(y = x^3 + 3x^2\).
Since both equations are equal to \(y\), set the right-hand sides equal to each other to eliminate \(y\): \(-4x + y = 12\) implies \(y = 4x + 12\) (by adding \$4x$ to both sides), so set \(4x + 12 = x^3 + 3x^2\).
Rewrite the equation to bring all terms to one side, forming a polynomial equation: \(x^3 + 3x^2 - 4x - 12 = 0\).
Solve the cubic equation \(x^3 + 3x^2 - 4x - 12 = 0\) by factoring or using methods such as the Rational Root Theorem to find possible roots for \(x\).
Once you find the values of \(x\), substitute each back into one of the original equations (for example, \(y = 4x + 12\)) to find the corresponding \(y\) values, giving you the solution pairs \((x, y)\).

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