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 7
Capitolo 6, Problema 7

In Exercises 5–18, solve each system by the substitution method. {x+3y=8y=2x−9\(\begin{cases}\) x + 3y = 8 \\ y = 2x - 9 \(\end{cases}\)

Guida verificata passo dopo passo
1
Identify the system of equations: \(\begin{cases} x + 3y = 8 \\ y = 2x - 9 \end{cases}\).
Since the second equation is already solved for \(y\), substitute \(y = 2x - 9\) into the first equation.
Replace \(y\) in the first equation: \(x + 3(2x - 9) = 8\).
Simplify and solve the resulting equation for \(x\): \(x + 6x - 27 = 8\).
Once you find \(x\), substitute it back into \(y = 2x - 9\) to find the value of \(y\).

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:
2m

Concetti chiave

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

System of Linear Equations

A system of linear equations consists of two or more linear equations with the same set of variables. The solution is the set of variable values that satisfy all equations simultaneously. Understanding how to interpret and represent these systems is fundamental to solving them.
Video consigliato:
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. It is especially useful when one equation is already solved for a variable.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

Solving Linear Equations

Solving linear equations means finding the value(s) of the variable(s) that make the equation true. This often involves isolating the variable using inverse operations like addition, subtraction, multiplication, or division. Mastery of these techniques is essential for solving systems after substitution.
Video consigliato:
04:02
Solving Linear Equations with Fractions
Pratica correlata
Domanda del libro di testo

Graph each inequality. y≤(1/3)x

618
views
Domanda del libro di testo

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. x3+x2(x2+4)2\(\frac{x^3 + x^2}{(x^2 + 4)^2}\)

737
views
Domanda del libro di testo

Solve each system in Exercises 5–18.

{x+y+2z=11x+y+3z=14x+2y−z=5\(\begin{cases}\) x + y + 2z = 11 \\ x + y + 3z = 14 \\ x + 2y - z = 5 \(\end{cases}\)

629
views
Domanda del libro di testo

In Exercises 1–18, solve each system by the substitution method.{x2+y2=25x−y=1\(\begin{cases}\) x^2 + y^2 = 25 \\ x - y = 1 \(\end{cases}\)

768
views
Domanda del libro di testo

Solve each system in Exercises 5–18. {4x−y+2z=11x+2y−z=−12x+2y−3z=−1\(\begin{cases}\) 4x - y + 2z = 11 \\ x + 2y - z = -1 \\ 2x + 2y - 3z = -1 \(\end{cases}\)

609
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.

578
views