Example of Solving a System of Linear Equations by Cramer's Rule.

This solution has been done by the calculator presented on the site.

It is necessary to solve the system of linear equations using Cramer's rule.
Знак системы3x1+3x2 = 9
x1 +2x2 = 9
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.
Let's calculate the determinant A.   more info
The determinant A consists of the coefficients of the left side of the system.
Знак системы3x1+3x2 = 9
x1 +2x2 = 9
det A = 3 3
1 2
= 3 * 2 - 3 * 1 = 6 - 3 = 3
The determinant A is not zero. It is possible to use the Cramer's rule.
Let's calculate the determinant A1.   more info
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
Знак системы3x1+3x2 = 9
x1 +2x2 = 9
3 3
1 2
9 3
9 2
det A1 = 9 3
9 2
= 9 * 2 - 3 * 9 = 18 - 27 = -9
Let's calculate the determinant A2.   more info
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
Знак системы3x1+3x2 = 9
x1 +2x2 = 9
3 3
1 2
3 9
1 9
det A2 = 3 9
1 9
= 3 * 9 - 9 * 1 = 27 - 9 = 18
Result:
x1 = det A1 / det A = -9/3 = -3
x2 = det A2 / det A = 18/3 = 6
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