In this case, x3 and x4 themselves can take any values To find solutions for the remaining two equations, x1 and x2 should be expressed in terms of x3 and x4. The last two equations are true for any values of the variables: System of linear equations which has an infinite number of solutions Using back substitution we find the only solution: System of linear equations which has a unique solutionĪfter bringing the matrix to a trapezoidal form by the Gauss method, we get: The default data below is the example of a system with an infinite number of solutions:ġ. The calculator finds a unique solution if it exists, or a general solution if an infinite number of solutions exist. The description of the Gaussian elimination method itself can be viewed at the link above, and below the calculator we look at the different systems of linear equations: those with one solution, with an infinite number of solutions, with no solution, and underdetermined and overdetermined systems. the previous calculator works only in the case when the number of equations is the same as the number of unknowns, and thus cannot solve underdetermined (the number of unknowns is greater than the number of equations) and overdetermined systems (the number of unknowns is less than the number of equations).Īs for the second and third points, the universality of the Gauss–Jordan elimination method makes it suitable for a systems of linear equations with any number of equations and unknowns.the previous calculator only determines the fact that there are an infinite number of solutions, but does not give a general solution.the previous calculator gives the solution in floating point format, while in many problem books the answer is usually given as a fraction.However, it has some disadvantages that the new calculator from this article will solve: The site already has one calculator that solves SLAE (System of Linear Algebraic Equations) by the Gauss–Jordan elimination (aka Gaussian elimination) method - Gaussian elimination.

Linear system of equations calculator