Algebra
3x3 System of Linear Equations Solver
Solve systems of 3 linear equations with 3 variables (x, y, z) easily online. Get step-by-step solutions and interactive visualizations for better understanding.
Enter Equations:
x + y + z =
x + y + z =
x + y + z =
Solution:
x ≈ , y ≈ , z ≈
3D Visualization:
Understanding Systems of Linear Equations
A system of linear equations is a set of equations where each equation is linear. For a 3x3 system, we have three equations with three variables (typically x, y, and z). The goal is to find values for these variables that satisfy all equations simultaneously.
Formulas and Concepts:
- Standard Form: Each linear equation is in the form ax + by + cz = d, where a, b, c are coefficients and d is the constant.
- Solution: The solution is a point (x, y, z) in 3D space where all three planes (represented by the equations) intersect.
- Methods to Solve: Common methods include substitution, elimination, and matrix methods (like the one used here, LU decomposition via math.js).
- Visualization: Each linear equation represents a plane in 3D space. The solution to the system is the intersection point of these planes. If the system has no solution, the planes do not intersect at a single point.
This tool uses the LU decomposition method from the math.js library to efficiently solve the system. The 3D visualization helps to understand the geometry of the equations and their solution.
Learn more about systems of linear equations on Wikipedia.