Solving systems of three linear equations in three variables
Systems of three linear equations in three variables 3x3
are the unknowns, a11
are the coefficients of the system, b1
are the constant terms
3x3 system of linear equations solver
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 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
By 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.
Divide the first equation by 3
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:
Divide the second equation by
Multiply (***) by
and add -1 times to the third equation.
The system we get
From the third equation z=3. Substitute this to the second equation:
Substituting y and z to the first equation, we get x
x=5, y=1, z=3