## Journal of Applied Mathematics and Statistical Applications

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Short Communication - Journal of Applied Mathematics and Statistical Applications (2018) Volume 1, Issue 2

## A new approach for solving linear equations with first order through derivatives

*Corresponding Author:
Rami Obeid
Head of data management and analysis division Central bank of Jordan, Jordan
Tel: 962-795-855-036
E-mail: [email protected]

Accepted date: September 17, 2018

Citation: Obeid R. A new approach for solving linear equations with first order through derivatives. J Appl Math Statist Appl. 2018;2(1):8-10.

### Abstract

This paper proposes a simple method to solve the first order linear equations, the proposed method is equivalent to classical Cramer’s rule for solving general systems of 2 linear equations, then it describes if there is a relationship between this method and the derivatives. The results show that there is a possible relationship between the method presented in this paper and the derivatives. Furthermore, we can use the first derivative to solve linear equations with first order.

### Keywords

Linear equations, Matrix, First derivatives, Cramer’s rule.

### Introduction

There are various methods to solve the linear equation, The Cramer's rule is the most common of these methods , Klein  described the approach based upon Cramer’s rule, the of the linear equation system can be written in matrix form: Ax =b , Cramer’s rule is efficient in solving systems of 2 linear equations. Some recent developments of using Cramer’s rule described in some papers, these papers can be found in [3-5] and the references therein.

Solving linear equations

First, this paper introduces a simple method for solving general systems of 2 linear equations, and we will prove it using Cramer's rule as following: Proof: We can prove the above rule by using Cramer's rule, as we know when we use Cramer's rule we find that:- (1)

and (2)

First, we want to prove that   Similarly, we can prove also that by using the above method.

The possible relation between rule 1 and the first derivative: -

Now we will discuss if there is a relation between rule 1 and derivatives: -

Using the same equation in rule (1):-   We can represent and by the following matrix:- Thus, if we want to find the values of x and y we can easily reach to the same results in Rule 1, where the two columns that we used to find x in rule 1 is similar to the coefficients of the constants and the variable y in the matrix of respectively:- Similarly, the two columns that we used to find y in rule 1 is similar to the coefficients of the variable x and the constants in the matrix of respectively: - Solving linear equations with first order by first derivatives

To explain how to solve linear equations with first order by first derivatives; suppose we have the following linear equation system: -

x + 2y = 4

3x − y =5

Let      49x =98⇒x = 2

Now to find the value of Y:-  49y = 49⇒y =1

### Conclusion

We have studied a simple method for solving systems of 2 linear equations. The method can be easily applied to systems of 2 linear equations. Also, we have described if there is a relationship between this method and the first derivative, the paper show that there is a possible relationship between them, and we can solve linear equations with first order by first derivatives.