Domanda del libro di testo
Graph each inequality. y>−3
662
views
Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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
Capitolo 6, Problema 11
In Exercises 1–18, solve each system by the substitution method.
Guida verificata passo dopo passo1
Start with the given system of equations: \(y^2 = x^2 - 9\) and \(2y = x - 3\).
From the second equation, solve for \(x\) in terms of \(y\): \(2y = x - 3\) implies \(x = 2y + 3\).
Substitute the expression for \(x\) from step 2 into the first equation: \(y^2 = (2y + 3)^2 - 9\).
Expand the right side: \((2y + 3)^2 = 4y^2 + 12y + 9\), so the equation becomes \(y^2 = 4y^2 + 12y + 9 - 9\).
Simplify and rearrange the equation to isolate terms and form a quadratic equation in \(y\): \(y^2 = 4y^2 + 12y\), then bring all terms to one side to solve for \(y\).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
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. It is especially useful when one equation is already solved or easily solvable for one variable.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics
Solving Quadratic Equations
Quadratic equations involve variables raised to the second power and can have two solutions. When substituting, the resulting equation may be quadratic, requiring methods like factoring, completing the square, or the quadratic formula to find solutions. Understanding how to solve quadratics is essential for finding all possible solutions.
Video consigliato:
06:08Solving Quadratic Equations by Factoring
Checking Solutions in Systems
After finding potential solutions, it is important to verify them by substituting back into the original equations. This ensures that the solutions satisfy both equations, especially since squaring or other operations can introduce extraneous solutions. Checking helps confirm the accuracy and validity of the answers.
Video consigliato:
6:19Systems of Inequalities
Pratica correlata
Domanda del libro di testo
Write the partial fraction decomposition of each rational expression. (3x +50)/(x -9)(x +2)
599
views
Domanda del libro di testo
Solve each system in Exercises 5–18.
648
views
Domanda del libro di testo
In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0
773
views
Domanda del libro di testo
Solve each system in Exercises 12–13. The is a piecewise function
618
views
Domanda del libro di testo
An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
658
views