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Chapter 1: Problem 114

What is an inconsistent equation? Give an example.

Short Answer

Expert verified
An inconsistent equation is a type of system of equations that has no solution. This happens when the represented lines on a graph do not intersect. An example of an inconsistent equation is: \[2x + 3y = 10\] and \[4x + 6y = 12\]. Despite having the same slopes, they will never intersect because they don't have the same y-intercepts.

Step by step solution

01

Definition of inconsistent equations

In algebra, an inconsistent equation is one that forms a system of equation which has no solution. This happens when the lines, represented on a graph by these equations, are parallel and do not intersect each other. A system of linear equations can be inconsistent if the slopes of the lines they represent are equal.
02

Providing an Example

An example of inconsistent equations is: \[ 2x+3y=10 \] \[ 4x+6y=12 \] If the equations are graphed, they would produce parallel lines.
03

Explaining the Example

In an inconsistent system, regardless of the number of equations or variables in the system, it's impossible to find a solution that satisfies all the equations at once. In the given example, both lines have the same slope (i.e., their ratio of y over x are equal: 3/2 = 6/4). But their y-intercepts are not equal (10/3 鈮� 12/6). So, the lines are parallel and will never intersect. Thus, there's no point (x, y) that satisfies both equations at the same time, making them inconsistent.

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