Consistent System Of Linear Equations Math

X 2y 2.

Consistent system of linear equations math. I if both the lines intersect at a point then there exists a unique solution to the pair of linear equations. A consistent system of equations has at least one solution and an inconsistent system has no solution. Algebraically if frac a 1 a 2 frac b 1 b 2 then the linear equations pair is consistent. The system x y 1 2x 2y 2 has infinitely many solutions as any x y pair will work so long as y x 1.

A consistent linear system is a system of linear equations with at least one set of values satisfying all equations. Watch an example of analyzing a system to see if it s consistent or inconsistent. In such a case the pair of linear equations is said to be consistent. Scroll down the page for more examples and solutions of consistent and inconsistent systems.

The lines in the system can be graphed together on the same coordinate graph and the solution to the system is the point at which the two lines intersect. In other words we can say a system of linear equations is nothing but two or more equations that are being solved simultaneously. Mostly the system of equations can be used by the business people to predict their future events. The following diagrams show consistent and inconsistent systems.

If you re seeing this message it means we re having trouble loading external resources on our website. In contrast a linear or non linear equation system is called inconsistent if there is no set of values for the unknowns that satisfies all of the equations. In the graph given above lines intersect at point p x y which represents the unique solution of the system of linear equations in two variables. More lessons for grade 11 algebra math worksheets examples solutions videos worksheets games and activities to help algebra students learn how to apply systems of linear equations.

System a is an independent linear system because neither of the equations in the system can be derived from the other equation. Consistent and inconsistent linear systems a system of linear equations is a set of linear equations which must be solved together. In mathematics a system of linear equations is a collection of two or more linear equations with the same set of variables in all the equations. In mathematics and particularly in algebra a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system that is when substituted into each of the equations they make each equation hold true as an identity.

For example x y 1 x 2y 5 has the solution x 3 y 4 and thus is consistent. System a is a consistent linear system because there is at least one solution.