Question

Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. $\begin{aligned} & 3 x-2 y=-15 \\ & x-\frac{2}{3} y=-5\end{aligned}$

Name: Problem 27, Chapter 3: McDougal Littell Algebra 2
Uploaded: 2022-03-17T01:23:01-08:00
Duration: 2 min 51 s
Channel: Erika Bustos
Description: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 3 x-2 y=-15 x-(2)/(3) y=-5

   Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.
$\begin{aligned} & 3 x-2 y=-15 \\ & x-\frac{2}{3} y=-5\end{aligned}$

McDougal Littell Algebra 2

Holt McDougal, Ron… 9th Edition

Chapter 3, Problem 27

Instant Answer

Solved by Expert Erika Bustos

03/17/2022

Step 1

The system of equations is: \[ \begin{aligned} & 3x - 2y = -15 \quad \text{(1)} \\ & x - \frac{2}{3}y = -5 \quad \text{(2)} \end{aligned} \] Show more…

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Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. $\begin{aligned} & 3 x-2 y=-15 \\ & x-\frac{2}{3} y=-5\end{aligned}$

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Key Concepts

Inconsistent Systems

These systems have no solution since the equations represent parallel or non-intersecting geometric objects, meaning there is no common point that satisfies all the equations.

Consistent and Dependent Systems

Such systems have infinitely many solutions because the equations describe the same geometric object; one equation is a multiple of the other, so every solution of one is also a solution of the other.

System of Linear Equations

A system of linear equations consists of two or more linear equations involving the same set of variables. The goal is to find values for these variables that satisfy all equations simultaneously.

Consistent and Independent Systems

These systems have exactly one unique solution, which means the geometric representations of the equations (lines, planes, etc.) intersect at exactly one point.

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