Solving systems of 3 linear equations in 3 variables

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Solving systems of three linear equations in three variables online

Systems of three linear equations in three variables

a11x1 + a12x2 + a13x3 = b1
a21x1 + a22x2 + a23x3 = b2
a31x1 + a32x2 + a33x3 = b3

where x1, x2, x3 are the unknowns, a11,..., a33 are the coefficients of the system, b1, b2, b3 are the constant terms

3x3 system of linear equations solver

This system solver can be used for solving systems of three linear equations in three variables or checking the solutions of 3 x 3 systems of linear equations solved by hand.

To solve a system of three linear equations with three unknowns using the online 3x3 system of equations solver, enter the coefficients of the three linear equations and click 'Solve'.

Solving a system of three linear equations in three variables using Cramer's rule

Example. Solving the system of three linear equations in three variables using Cramer's rule.

system of three equations

Cramer's rule to solve the system of three equations

By Cramer's rule:

Solve the system of three equations with Cramer's rule

Solving systems of three equations using Gaussian Elimination

Solving a system of linear equations using Gaussian Elimination

Example. Solving the system of three linear equations in three variables using Gaussian Elimination.

system of three equations
Divide the first equation by 3

solve system of three equations

Multiply (**) by 4 and add -1 times to the second equation, then multiply (**) by (-1) and add to the third equation. We get the following system:

Solve systems of three equations by Gaussian Elimination

Divide the second equation by and get Solve systems of equations with three unknowns by Gaussian Elimination

Multiply (***) by and add -1 times to the third equation.

The system we get Gaussian Elimination to solve systems of three equations

From the third equation z=3. Substitute this to the second equation: => y=1>

Substituting y and z to the first equation, we get x => x=5

x=5, y=1, z=3

Thursday, July 24, 2014

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