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 3
Capitolo 6, Problema 3

Determine if the given ordered triple is a solution of the system. (4,1,2)(4, 1, 2)
{x−2y=22x+3y=11y−4z=−7\(\begin{cases}\) x - 2y = 2 \\ 2x + 3y = 11 \\ y - 4z = -7 \(\end{cases}\)

Guida verificata passo dopo passo
1
Identify the system of equations and the ordered triple given: the system is \( x - 2y = 2 \), \( 2x + 3y = 11 \), and \( y - 4z = -7 \), and the ordered triple is \( (4, 1, 2) \) where \( x=4 \), \( y=1 \), and \( z=2 \).
Substitute the values of \( x \), \( y \), and \( z \) from the ordered triple into the first equation: \( x - 2y = 2 \) becomes \( 4 - 2(1) = ? \).
Check if the left side equals the right side in the first equation after substitution to verify if it holds true.
Repeat the substitution process for the second equation \( 2x + 3y = 11 \) by plugging in \( x=4 \) and \( y=1 \), then verify if the equation is satisfied.
Finally, substitute \( y=1 \) and \( z=2 \) into the third equation \( y - 4z = -7 \) and check if the equality holds. If all three equations are true, the ordered triple is a solution; otherwise, it is not.

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.

Ordered Triple as a Solution

An ordered triple (x, y, z) represents values for variables in a system of equations with three variables. To verify if it is a solution, substitute each value into the corresponding variables in all equations and check if all equations hold true.
Video consigliato:
3:31
Example 2

Substitution Method

Substitution involves replacing variables in equations with given values or expressions. Here, substituting x=4, y=1, and z=2 into each equation tests whether the left-hand side equals the right-hand side, confirming if the triple satisfies the system.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

System of Linear Equations

A system of linear equations consists of multiple linear equations involving the same variables. Solutions are values that satisfy all equations simultaneously. Understanding how to work with such systems is essential for determining if a given triple is a solution.
Video consigliato:
4:27
Introduction to Systems of Linear Equations
Pratica correlata
Domanda del libro di testo

In Exercises 1–4, determine whether the given ordered pair is a solution of the system. (2, 5) 2x + 3y = 17 x + 4y = 16

1107
views
Domanda del libro di testo

Find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=40x+50y

511
views
Domanda del libro di testo

In Exercises 1–18, solve each system by the substitution method. {x+y=2y=x2−4x+4\(\begin{cases}\) x + y = 2 \\ y = x^2 - 4x + 4 \(\end{cases}\)

547
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. 6x2−14x−27(x+2)(x−3)2\(\frac{6x^2-14x-27}{\left(x+2\right)(x-3)^2}\)

722
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. (3x+16)/(x + 1) (x − 2)²

736
views
Domanda del libro di testo

Graph each inequality. x−2y>10

601
views