# Service for Solving Linear Programming Problems

and other interesting typical problems
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## Example №1. Solving of a 2x2 System of Linear Equations by the Cramer's Rule

This solution has been made using the calculator presented on the site.
It is necessary to solve the system of linear equations using Cramer's rule. 3 x1 - x2 = -14 x1 + x2 = 2
Let's write the Cramer's rule:
x1 = det A1 / det A
x2 = det A2 / det A
It is impossible to divide by zero. Therefore, if the determinant of A is zero, then it is impossible to use Cramer's rule.
The determinant A consists of the coefficients of the left side of the system. 3 x1 - x2 = -14 x1 + x2 = 2
 det A = 3 -1 1 1
= 3 * 1 - ( -1) * 1 = 3 + 1 = 4
The determinant A is not zero. It is possible to use the Cramer's rule.
It is necessary to change column 1 in determinant A to the column of the right side of the system.
System det A det A1 3 x1 - x2 = -14 x1 + x2 = 2
 3 -1 1 1
 -14 -1 2 1
 det A1 = -14 -1 2 1
= -14 * 1 - ( -1) * 2 = -14 + 2 = -12
It is necessary to change column 2 in determinant A to the column of the right side of the system.
System det A det A2 3 x1 - x2 = -14 x1 + x2 = 2
 3 -1 1 1
 3 -14 1 2
 det A2 = 3 -14 1 2
= 3 * 2 - ( -14) * 1 = 6 + 14 = 20
Result:
x1 = det A1 / det A = -12/4 = -3
x2 = det A2 / det A = 20/4 = 5