Skip to main content
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 19
Capitolo 6, Problema 19

In Exercises 19–28, solve each system by the addition method. {x2+y2=13x2−y2=5\(\begin{cases}\) x^2 + y^2 = 13 \\ x^2 - y^2 = 5 \(\end{cases}\)

Guida verificata passo dopo passo
1
Identify the given system of equations: \\ \(x^2 + y^2 = 13\) and \(x^2 - y^2 = 5\).
Add the two equations together to eliminate \(y^2\(: \\ \)(x^2 + y^2) + (x^2 - y^2) = 13 + 5\).
Simplify the resulting equation: \\ \(2x^2 = 18\).
Solve for $x^2\( by dividing both sides by 2: \\ \)x^2 = 9$.
Substitute \(x^2 = 9\) back into one of the original equations (for example, \(x^2 + y^2 = 13\)) to solve for \(y^2\), then find \(y\).

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:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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. Understanding how to interpret and manipulate these systems is essential for finding their solutions.
Video consigliato:
4:27
Introduction to Systems of Linear Equations

Addition Method (Elimination Method)

The addition method involves adding or subtracting equations to eliminate one variable, simplifying the system to a single equation with one variable. This technique is useful when the coefficients of a variable are opposites or can be made opposites by multiplication.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

Solving Quadratic Equations

Quadratic equations involve variables raised to the second power. Solving them may require factoring, using the quadratic formula, or simplifying expressions after elimination. Recognizing and solving quadratic forms is crucial when variables appear squared in systems.
Video consigliato:
06:08
Solving Quadratic Equations by Factoring
Pratica correlata
Domanda del libro di testo

Find the quadratic function y = ax2+bx+c whose graph passes through the given points. (−1, 6), (1, 4), (2, 9)

801
views
Domanda del libro di testo

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

802
views
Domanda del libro di testo

Graph each inequality. y < x2 - 1

558
views
Domanda del libro di testo

In Exercises 19–30, solve each system by the addition method. x + y = 1 x - y = 3

870
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. 4x2 - 7x - 3/(x3 -x)

723
views
Domanda del libro di testo

In Exercises 1–18, solve each system by the substitution method. {x+y=1(x−1)2+(y+2)2=10\(\begin{cases}\) x + y = 1 \\ (x - 1)^2 + (y + 2)^2 = 10 \(\end{cases}\)

564
views