When is a line consistent

Thus, we can say that there are infinitely many solutions for the system of equations. Often we attempt to solve that system but end up with an equation that makes no sense mathematically because these equations are empty of any acceptable solution. Like for example,. With the help of the matrix method we can solve the above equation as follows:. The reduction of the above matrix to Row Echelon form can be done as follows:. Now by Adding row 2 to row 1, we get:.

The equation sketched out from the second row of the matrix is given as. We know that the above result is mathematically impossible and it can be said that the equation has no solution. In order to solve the variable in a system of equations, elimination method is used to eliminate the remaining variables. This elimination method is also known as elimination by addition. So, to find the correct value for the other variable it is substituted to the original equation after the values for the remaining variables are found.

Given Below are the Steps of the Elimination Method:. You can conclude that the system offers endless solutions. This is known as the coherent system. A system without solutions is called an inconsistent system. So how do you know if a system is consistent or inconsistent? If a coherent system has exactly one solution, it is independent.

Whether a coherent system has an infinite number of solutions depends on it. When plotting equations, both equations represent the same line. When a system has no solution, there is an inconsistency. So the question is, which system of equations is inconsistent? A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel.

A system of dependent equations arises when the same line is written in two different forms such that there are infinite solutions. What do we mean by coherent and inconsistent in this context? If so, the pairs of linear equations are algebraically consistent. Are plumb lines consistent or inconsistent? Definitions: If the two equations describe lines that intersect once, the system is independent and coherent.

If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Varsity Tutors connects learners with experts.