Solve 2x2 and 3x3 systems of equations with this free system of equations calculator. Find unique solutions, inconsistent systems, dependent systems, and matrix steps instantly.
Elimination:
Add or subtract equations to remove a variable.
Substitution:
Solve one equation for one variable, then substitute.
Matrix method:
Use row operations or determinants to solve the system.
This calculator detects whether the system has one solution, no solution, or infinitely many solutions.
Systems of equations model multiple conditions happening at the same time. They are used in algebra, physics, economics, engineering, and optimization problems.
They help find values that satisfy several equations at once.
Your result shows whether the system has a unique solution, no solution, or infinitely many solutions. It also includes matrix form and solving steps for easier checking.
For 2-variable systems, the solution is the intersection point of the two lines. For 3-variable systems, the solution is the point where all three planes meet.
A system of equations is a set of equations solved together to find values that satisfy all of them.
If the equations lead to a contradiction such as 0 = 5, the system has no solution.
If one equation is a multiple of another and they represent the same relationship, the system can have infinitely many solutions.
It depends on the system. Elimination is often fastest, while matrix methods are useful for organization and larger systems.