Independent and consistent systems

A consistent system of equations has at least one solution, and an inconsistent system has no solution. When you graph the equations, both equations represent the same line. The graphs of the lines do not intersect, so the graphs . That means that those equations intersect only at that one point. That kind of solution is called consistent and independent !

This tutorial explains systems with one solution and even shows you an example!

If the system has no solution, then it is said to be inconsistent system.

The following figure will give clear picture of what we have learnt above. Examples: Discuss the number of solutions and type of the system of equations given in the graphs. Independent systeone solution and one intersection point. Inconsistent systeno solution and no intersection point.

An example is: State whether each system is consistent and dependent , . All examples shown are linear systems. You can put this solution on YOUR website! What is the difference between: independent and dependent.

All the systems of equations that we have seen in this section so far have had unique solutions. The equations can be viewed algebraically or graphically. What are those systems calle and where would they be found in the real . But if this is not possible, then that equation is independent of the . A system of equations whose left-hand sides are linearly independent is always consistent. Putting it another way, according . This video looks at classifying systems of equations ( consistent , inconsistent , independent , dependent ) and determining the number of solutions without graph.

In other words, they end up being the same line. View profile for: thepurplellama3. Sal can explain it better than me.

In mathematics and in particular in algebra, a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the system —that is, that when substituted into each of the equations makes the equation hold true as an identity.