Example №1. Solving of a 2x2 System of Linear Equations by the Cramer's RuleThis solution was made using the calculator presented on the site. It is necessary to solve the system of linear equations using Cramer's rule.
Let's write the Cramer's rule: x_{1} = det A_{1} / det A x_{2} = det A_{2} / 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. Let's calculate the determinant A. more info The determinant A consists of the coefficients of the left side of the system.
= 3 * 1  ( 1) * 1 = 3 + 1 = 4
The determinant A is not zero. It is possible to use the Cramer's rule. Let's calculate the determinant A_{1}. more info It is necessary to change column 1 in determinant A to the column of the right side of the system.
= 14 * 1  ( 1) * 2 = 14 + 2 = 12
Let's calculate the determinant A_{2}. more info It is necessary to change column 2 in determinant A to the column of the right side of the system.
= 3 * 2  ( 14) * 1 = 6 + 14 = 20
Result: x_{1} = det A_{1} / det A = 12/4 = 3 x_{2} = det A_{2} / det A = 20/4 = 5
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