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

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 \(\end{cases}\)

Guida verificata passo dopo passo
1
Write down the system of equations clearly: \[4x - 0y + 2z = 11\] \[x + 2y - z = -1\] \[2x + 2y - 3z = -1\]
Since the first equation has no y term, focus on expressing one variable in terms of the others from one of the simpler equations. For example, from the second equation, solve for \(x\) in terms of \(y\) and \(z\): \[x = -1 - 2y + z\]
Substitute the expression for \(x\) from step 2 into the first and third equations to eliminate \(x\). This will give you two equations with only \(y\) and \(z\) as variables.
Solve the resulting two-variable system from step 3 using either substitution or elimination to find values for \(y\) and \(z\).
Once you have \(y\) and \(z\), substitute these values back into the expression for \(x\) from step 2 to find the value of \(x\). This completes the solution for the system.

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:
6m

Concetti chiave

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

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with the same variables. The goal is to find values for the variables that satisfy all equations simultaneously. Understanding how to interpret and set up these systems is essential for solving them.
Video consigliato:
4:27
Introduction to Systems of Linear Equations

Methods for Solving Systems (Substitution, Elimination, and Matrix Methods)

Common techniques to solve systems include substitution, elimination, and using matrices (such as Gaussian elimination). These methods help reduce the system to simpler forms, making it easier to find the values of variables that satisfy all equations.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

Consistency and Types of Solutions

A system can have one unique solution, infinitely many solutions, or no solution. Recognizing the system's consistency helps determine the nature of the solution set, which is crucial when interpreting the results of solving the system.
Video consigliato:
05:17
Types of Slope
Pratica correlata
Domanda del libro di testo

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

774
views
Domanda del libro di testo

Graph each inequality. y>2x−1

624
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

A chemist needs to mix a solution that is 34% silver nitrate with one that is 4% silver nitrate to obtain 100 milliliters of a mixture that is 7% silver nitrate. How many milliliters of each of the solutions must be used?

954
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

In Exercises 1–8, write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. (7x2 -9x+3)/(x2+7)2

811
views