Calculator of Cramer's Rule 2x2

Example №1. Solving of a 2x2 System of Linear Equations by the Cramer's Rule

This solution was 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.

Let's calculate the determinant A. more info

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.

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

		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

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

		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