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 27
Capitolo 6, Problema 27

In Exercises 19–30, solve each system by the addition method. 3x - 4y = 11 2x + 3y = - 4
Exercise 27: Solve the system of equations 3x - 4y = 11 and 2x + 3y = -4 using the addition method.

Guida verificata passo dopo passo
1
Step 1: Write down the system of equations clearly: 3x-4y=112x+3y=-4.
Step 2: To use the addition method, multiply each equation by a suitable number so that the coefficients of either x or y are opposites. For example, multiply the first equation by 3 and the second equation by 4 to align the coefficients of y: 3(3x - 4y) = 3(11) and 4(2x + 3y) = 4(-4).
Step 3: After multiplication, the system becomes: 9x - 12y = 33 and 8x + 12y = -16. Now add the two equations to eliminate y: (9x - 12y) + (8x + 12y) = 33 + (-16).
Step 4: Simplify the resulting equation to solve for x. Once you find x, substitute it back into one of the original equations to solve for y.
Step 5: Write the solution as an ordered pair (x, y) representing the values of x and y that satisfy both 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:
3m

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 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

Addition (Elimination) Method

The addition method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable. This requires manipulating the equations, often by multiplying by constants, to align coefficients for elimination.
Video consigliato:
6:04
How to Multiply Equations in Elimination Method

Solving for Variables After Elimination

Once a variable is eliminated, the resulting single-variable equation is solved using basic algebra. After finding one variable, substitution back into one of the original equations allows solving for the other variable, completing the solution to the system.
Video consigliato:
6:48
Solving Systems of Equations - Elimination
Pratica correlata
Domanda del libro di testo

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

{3x+6y≤62x+y≤8\(\begin{cases}\) 3x + 6y \(\leq\) 6 \\ 2x + y \(\leq\) 8 \(\end{cases}\)

557
views
Domanda del libro di testo

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

536
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. x2+2x+7/x(x − 1)2

743
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. x2/(x − 1)2 (x + 1)

688
views
Domanda del libro di testo

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

521
views
Domanda del libro di testo

Solve each system in Exercises 25–26. {x+32−y−12+z+24=32x−52+y+13−z4=−256x−34−y+12+z−32=−52\(\begin{cases}\) \(\frac{x + 3}{2}\) - \(\frac{y - 1}{2}\) + \(\frac{z + 2}{4}\) = \(\frac{3}{2}\) \\ \(\frac{x - 5}{2}\) + \(\frac{y + 1}{3}\) - \(\frac{z}{4}\) = - \(\frac{25}{6}\) \\ \(\frac{x - 3}{4}\) - \(\frac{y + 1}{2}\) + \(\frac{z - 3}{2}\) = - \(\frac{5}{2}\) \(\end{cases}\)

630
views