Question

Define

Instructions:

After reading Chapter 4 of the textbook, define the following terms:

-System of linear equations

-Solution to a system of equations

-Consistent system of equations

-Inconsistent system of equations

Write a good paragraph with at least 5 sentences using a minimum of 75 words.

Answer 1

System of linear equations:

system of linear equation is a collection of two or more linear equationsinvolving the same set of variables. An equation in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero (a² + b² ≠ 0), is called a linear equation in two variable.

Solution to a system of equations:

Every solution of the equation is a point on the line representing it.
Each solution (x, y) of a linear equation in two variables, ax + by + c = 0, corresponds to a point on the line representing the equation, and vice versa.

system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of theequations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set.

Consistent system of equations:

A consistent system is a system that has at least one solution.

For Consistent Systems of Equations, i.e. for a given system, if there exists one solution set for the different variables in the system or infinitely many sets of solution. In other words, as long as we can find a solution for the system of equations, we refer to that system as being consistent.

For a two variable system of equations to be consistent the lines formed by the equations have to meet at some point or they have to be parallel.

For a three variable system of equations to be consistent, the equations formed by the equations must meet two conditions:

1. All three planes have to parallel
2. Any two of the planes have to be parallel and the third must meet one of the planes at some point and the other at another point.

Inconsistent system of equations:

Inconsistent Systems of Equations arises when for a given set of variables,if there in no set of solutions for the system of equations.

Inconsistent systems arise when the lines or planes formed from the systems of equations don't meet at any point and are not parallel (all of them or only two and the third meets one of the planes at some point.)