Problem 85 - College Algebra

Question

What is an inconsistent equation? Give an example.

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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'.