3×3 System of Equations Calculator

Enter a system of three linear equations to find its solution.


With this calculator, you can find the solution to a system of three equations with three variables. Enter the equations and the solution will be displayed at the bottom.

How to use the systems of three equations calculator?

Step 1: Enter each of the equations in its respective input box. You can use equations with any variables as long as the variables are consistent throughout the system.

Step 2: Click “Solve” to get the solution to the system of equations.

Step 3: The solution along with the system of three equations entered will be displayed at the bottom.

What kind of systems of equations can I solve on the calculator?

For now, the calculator only supports systems of linear equations. This means that we can only enter equations of the type x+y+z=1. However, you can enter the equations in any order. The equations x=2y+z+5 as well as 2x+2y=3z+5 are supported.

Quadratic, trigonometric, logarithmic equations, or any type of equations that are not linear are not supported.

What are 3×3 systems of equations?

3×3 systems of equations are systems of three equations with three variables. These systems are characterized in that all their equations share the same solution.

To find a solution to a 3×3 system, the equations have to be solved simultaneously and the solution has to satisfy all three equations at the same time.

How to solve systems of three equations with three unknowns?

A system of three equations with three variables can be solved by using a series of steps that cause one variable to be eliminated. The steps include swapping the order of the equations, multiplying both sides of the equation by a nonzero constant, and adding a multiple of one equation to the other equation.

Other methods for solving systems of three equations with three unknowns include using matrices and linear algebra. Through the use of matrices we can not only solve systems of three equations but even larger systems with more variables.

However, as the systems get larger, the manual solution becomes much more complicated, so we have to use numerical methods and use a computer.

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