Ch. 5 - Systems of Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 5 - Systems of Equations and Inequalities

Problema 35

Capitolo 6, Problema 35

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x - 2y = − 5 4x + y = 8

Guida verificata passo dopo passo

Start by writing down the system of equations clearly:

3x - 2 y = - 5

and

4 x + y = 8

Choose a method to solve the system. Here, substitution or elimination are both good options. For elimination, aim to eliminate one variable by making the coefficients of either

x

y

opposites.

Multiply the second equation by 2 to align the coefficients of

y

2(4x + y) = 2(8)

which gives

8x + 2y = 16

Add the first equation

3x - 2y = -5

and the new equation

8x + 2y = 16

to eliminate

y

(3x + 8x) + (-2y + 2y) = -5 + 16

Solve the resulting equation for

x

, then substitute this value back into one of the original equations to find

y

. Finally, check if the system has one solution, no solution, or infinitely many solutions by analyzing the consistency of the equations.

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:

Concetti chiave

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

Solving Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. Solving the system means finding values for the variables that satisfy all equations simultaneously. Common methods include substitution, elimination, and graphing.

Video consigliato:

4:27

Introduction to Systems of Linear Equations

Types of Solutions for Systems

Systems of linear equations can have one solution (consistent and independent), no solution (inconsistent), or infinitely many solutions (dependent). Identifying the type depends on the relationships between the equations, such as parallel lines or coincident lines.

Video consigliato:

6:19

Systems of Inequalities

Expressing Solution Sets Using Set Notation

Set notation is a concise way to represent the solution(s) of a system. For a unique solution, it lists the ordered pair; for infinitely many solutions, it expresses the solution in terms of a parameter; and for no solution, the solution set is the empty set, denoted by ∅.

Video consigliato:

07:07

Introduction to Exponents

Pratica correlata

Domanda del libro di testo

Graph the solution set of each system of inequalities or indicate that the system has no solution.

$\begin{cases}\) x $\leq$ 2 \\ y $\geq$ -1 \(\end{cases}$

544

views

Domanda del libro di testo

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

497

views

Domanda del libro di testo

The perimeter of a rectangle is 26 meters and its area is 40 square meters. Find its dimensions.

887

views

Domanda del libro di testo

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + 3y = 2 3x + 9y = 6

793

views

Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. 6x²-x+1/(x³ + x²+ x +1)

711

views

Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. $\frac{x^3 + x^2 + 2}{(x^2 + 2)^2}$

745

views