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Linear Equation Calculator

Solve ax + b = 0 or a 2×2 linear system — full-width layout with sidebar like conversion tools.

How it works

The linear equation calculator solves linear equations in one or two variables. For one variable: ax + b = 0. For two variables: solves systems of two linear equations.


The Formula

One variable: x = -b/a\nTwo variables: Using Cramer's rule or elimination method
  • a, b

    Coefficients in ax + b = 0

  • a₁, b₁, c₁

    Coefficients in first equation

  • a₂, b₂, c₂

    Coefficients in second equation


Worked Example

  1. Example 1: Solve 2x + 4 = 0

    x = -4/2 = -2

  2. Example 2: Solve system: x + y = 5, 2x - y = 1

    Adding equations: 3x = 6, so x = 2 Substituting: 2 + y = 5, so y = 3


Tips, Assumptions & Limitations

  • For one variable: if a = 0 and b = 0, infinite solutions; if a = 0 and b ≠ 0, no solution.
  • For two variables: determinant must be non-zero for unique solution.
  • Results are displayed with 4 decimal places precision.

To solve a linear equation with two variables, you can use the linear equation calculator by entering the coefficients of the variables and the constant term. The calculator will then provide a step-by-step solution to the equation. You can also enter multiple equations and the calculator will solve the system of equations.

The format for entering equations into the calculator is straightforward. For a simple equation, enter the coefficients and constants in the standard form, such as ax + by = c. For multiple equations, separate each equation with a comma or on a new line.

Yes, the linear equation calculator can solve systems of linear equations. To do this, enter each equation separately, making sure to include all variables and constants. The calculator will then provide a solution to the system, if one exists.

The results from the linear equation calculator will provide the solution to the equation or system of equations. If there is a single solution, it will be displayed as the value of the variable. If there are multiple solutions, they will be listed. In some cases, the calculator may indicate that there is no solution or that the solution is infinite.

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