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Chapter 1: Problem 85

What is an inconsistent equation? Give an example.

Short Answer

Expert verified
An inconsistent equation is a system of equations that has no solution, meaning there are no common points that satisfy all the equations in the system. An example would be the system of equations: y = 2x + 5 and y = 2x + 8. These parallel lines never intersect and therefore, have no common solutions.

Step by step solution

01

Understanding an Inconsistent Equation

An inconsistent equation is a system of equations that do not have a solution. That is, no set of values exist that can satisfy all equations of the system simultaneously. In terms of graphical interpretation, if the system represents a set of lines, these lines do not intersect at any point, hence they are parallel.
02

Example of Inconsistent Equation

Let's take an example. Consider the system of equations: \[y = 2x + 5\] and \[y = 2x + 8\]. The slopes of the lines are equal (2) but the y-intercepts are different (5 and 8), which means these lines are parallel and never intersect. Hence, this system of equation is 'inconsistent'.

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Most popular questions from this chapter

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\sqrt{-8}(\sqrt{-3}-\sqrt{5})$$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$(-3-\sqrt{-7})^{2}$$

Describe similarities and differences between the solutions of $$ (x-2)(x+5) \geq 0 \text { and } \frac{x-2}{x+5} \geq 0 $$

In Exercises \(1-16,\) solve and check each linear equation. $$ 7 x-5=72 $$

What is a rational inequality?
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