​​The ESolver is an iOS application that can generate an explicit solution of a linear system that has less than six equations. The solution is presented in a multilevel folded pattern that allows users to have a better understanding of an operation.

The style of the solution includes self-explanatory directive steps where a step may contain one or more steps. And this process may be repeated until a certain elementary algebraic operation (e.g. addition, subtraction, etc.) is reached.The current version of the ESolver, also provides a feature to generate sample systems using the Generate button, which is a great way to learn how to enter equations to the Workspace. The Validate button is the key to turn on the Solution navigation button. If validation fails, the Solution button will not be activated. To get a successful validation message, users need to follow all the rules that apply to entering the equations.

There are four different solvers that are available for you, which are:

• Substitution of Variables: this allows you to solve a linear system using substitution of variable technique.
• ​Elimination of Variables-Addition: this allows you to solve a linear system by successive elimination of variables. The elimination is done via adding two equations.
• Elimination of Variables-Subtraction: this allows you to solve a linear system by successive elimination of variables. The elimination is done via subtraction.
• Just give me the solution: this provides you with just the answer of a solvable linear system.

This is a great app that can be used by students as a self-learning tool and by instructors for illustration purposes. We do not guarantee that it is completely bug free. So, you should not use the solution in any way that may put any of your valuables at risk. But we are working every day to make this app better.

To obtain the solution an internet connection is not required.

#### Sample Solution:

Numbering the entered equations:

Reorganizing the system:
 52X1 + 32X2 + 3X3 = 854 ... 6 Same as 3 2X1 - 32X2 + 3X3 = 252 ... 7 Same as 4 5X1 - X2 + 2X3 = 2 ... 8 Same as 5 X1 + 72X2 + X3 + 2X4 - 2X5 = -3 ... 9 Same as 2 X1 + X2 + 4X3 - 12X4 - 2X5 = 17 ... 10 Same as 1

Eliminating variable X1 from equation 6 and 7
We have,
 52X1 + 32X2 + 3X3 = 854 2X1 - 32X2 + 3X3 = 252

Multiplying the first and second equations by -2 and 52 respectively we get,

Adding these two equations we get,

Eliminating variable X1 from equation 7 and 8
We have,
 2X1 - 32X2 + 3X3 = 252 5X1 - X2 + 2X3 = 2

Multiplying the first and second equations by -5 and 2 respectively we get,

Adding these two equations we get,

Eliminating variable X2 from equation 11 and 12
We have,
 -274X2 + 32X3 = -454 112X2 - 11X3 = -1172

Multiplying the first and second equations by -112 and -274 respectively we get,

Adding these two equations we get,

Solving equation 13 for variable X3 we get,
Substituting the value of variable X3 from equation 14 into 11 we get,
Substituting the value of variables X3 and X2 from equations 14 and 15 into 6 we get,

Substituting the value of variables X3, X2 and X1 from equations 14, 15 and 16 into 9 and 10 we get,

Eliminating variable X4 from equation 17 and 18
We have,
 -2X4 + 2X5 = 42722 12X4 + 2X5 = 53544

Multiplying the second equation by 4 we get,

Adding these two equations we get, 