*Kathryn White has over 11 years of experience tutoring a range of subjects at the kindergarten through college level.*Her writing reflects her instructional ability as well as her belief in making all concepts understandable and approachable.

A system of linear equations involves two relationships with two variables in each relationship.

By solving a system, you are finding where the two relationships are true at the same time, in other words, the point where the two lines cross.

To create this article, volunteer authors worked to edit and improve it over time. This article can explain how to perform to achieve the solution for both variables.

Have you ever had a simultaneous problem equation you needed to solve?

Methods for solving systems include substitution, elimination, and graphing.

Each one will give the right answer but is more or less useful depending on the problem and situation.

In contrast, if neither equation has Y isolated, you are better off using substitution or elimination.

Using a graphing calculator to enter both equations and find the point of intersection comes in handy when they involve decimals or fractions.

We perform elemental operations in the rows to obtain the reduced row echelon form: We multiply the first row by 1/5 and the second by 1/3 We add the second row with the first We multiply the second row by 5/7 We add the first row with the second one multiplied by -2/5 This last equivalent matrix is in the reduced row echelon form and it allows us to quickly see the rank of the coefficient matrix and the augmented one.

We calculate the ranks: By the Rouché-Capelli theorem, the system is consistent Independent.

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