Question

Explain how you can tell by observation that the following system is inconsistent. $$ \begin{aligned} &-x+3 y=5 \\ &2 x-6 y=-13 \end{aligned} $$

Name: Problem 90, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2020-06-04T22:22:04-08:00
Duration: 2 min 46 s
Channel: Matt Gibson
Description: Explain how you can tell by observation that the following system is inconsistent. -x+3 y=5 2 x-6 y=-13

   Explain how you can tell by observation that the following system is inconsistent.
$$
\begin{aligned}
&-x+3 y=5 \\
&2 x-6 y=-13
\end{aligned}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 90

Instant Answer

Solved by Expert Matt Gibson

06/04/2020

Step 1

In the first equation, the coefficients are -1 for x and 3 for y. In the second equation, the coefficients are 2 for x and -6 for y. Show more…

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Explain how you can tell by observation that the following system is inconsistent. $$ \begin{aligned} &-x+3 y=5 \\ &2 x-6 y=-13 \end{aligned} $$

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Key Concepts

Inconsistent Systems

An inconsistent system is one where no single solution satisfies all the equations simultaneously. This occurs when the equations, when interpreted as geometric objects like lines, do not intersect at any point.

Parallel Lines

When the equations of a system of linear equations represent lines, a key observation is whether the lines are parallel. If the lines have the same slope but different intercepts, they never meet, indicating an inconsistency within the system.

Proportional Coefficients

A useful method for identifying an inconsistent system is by comparing the coefficients of the variables. If the ratios of the coefficients of the variables are the same across equations, while the ratios to the constants differ, it implies that the lines are parallel, yielding no solution for the system.

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