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 17
Capitolo 6, Problema 17

In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2
Two equations for a system of linear equations: y = (1/3)x + 2/3 and y = (5/7)x - 2.

Guida verificata passo dopo passo
1
Step 1: Since both equations are equal to y, set the right-hand sides of the equations equal to each other: 13x + 23 = 57x - 2.
Step 2: To solve for x, first eliminate the fractions by finding a common denominator or multiply both sides of the equation by the least common multiple of the denominators (which is 21) to clear the fractions.
Step 3: After clearing the fractions, simplify the resulting equation and isolate the variable x on one side.
Step 4: Solve the simplified linear equation to find the value of x.
Step 5: Substitute the value of x back into either original equation (for example, y = 13x + 23) to find the corresponding 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:
4m

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 values that satisfy all equations simultaneously. Graphically, this corresponds to the point(s) where the lines intersect.
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.
Video consigliato:
04:03
Choosing a Method to Solve Quadratics

Slope-Intercept Form

Equations in slope-intercept form are written as y = mx + b, where m is the slope and b is the y-intercept. Understanding this form helps in interpreting the equations and solving systems by substitution or graphing.
Video consigliato:
03:56
Slope-Intercept Form
Pratica correlata
Domanda del libro di testo

Solve each system in Exercises 5–18. {3(2x+y)+5z=−12(x−3y+4z)=−94(1+x)=−3(z−3y)\(\begin{cases}\) 3(2x + y) + 5z = -1 \\ 2(x - 3y + 4z) = -9 \\ 4(1 + x) = -3(z - 3y) \(\end{cases}\)

652
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. 4x2+13x-9/x (x − 1)(x+3)

709
views
Domanda del libro di testo

Graph each inequality. (x−2)2+(y+1)2<9

634
views
Domanda del libro di testo

In Exercises 16–24, write the partial fraction decomposition of each rational expression. (4x^2 - 3x - 4)/x(x + 2)(x - 1)

802
views
Domanda del libro di testo

Graph each inequality. y < x2 - 1

558
views
Domanda del libro di testo

In Exercises 1–18, solve each system by the substitution method. {x+y=1(x−1)2+(y+2)2=10\(\begin{cases}\) x + y = 1 \\ (x - 1)^2 + (y + 2)^2 = 10 \(\end{cases}\)

564
views