교과서 질문
In Exercises 47–52, solve each system by the method of your choice.
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Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
6장, 문제 49
In Exercises 47–52, solve each system by the method of your choice.
검증된 단계별 안내1
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 \((x, y)\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
5m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Systems of Equations
A system of equations consists of two or more equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. Solutions can be points where the graphs of the equations intersect.
추천 영상:
4:27
Introduction to Systems of Linear Equations
Substitution Method
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation. This reduces the system to a single equation with one variable, making it easier to solve.
추천 영상:
04:03Choosing a Method to Solve Quadratics
Solving Nonlinear Equations
When a system includes nonlinear equations, such as cubic or quadratic terms, solving requires careful algebraic manipulation. After substitution, the resulting equation may be polynomial, requiring factoring or other methods to find roots.
추천 영상:
3:21Nonlinear Inequalities
관련 실천
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