# Equation Solver

Solve a system of linear equations with up to 10 equations and 10 unknowns. Type one equation per line, such as 2x + y = 7, and the solver finds the variables, eliminates them with exact fractions using mathjs and reports a unique solution, no solution or infinitely many solutions with a parametric form. Decimals are rounded to the places you choose. Great for algebra, linear systems homework and quick checks of hand calculations.

## Frequently asked questions

### How do I enter a system of equations?

Write one equation per line, or separate equations with semicolons, for example 2x + y = 7 on one line and x - y = -1 on the next. Each equation may contain one equals sign, and an equation without one is read as expression = 0. Implicit multiplication such as 2x is understood.

### Which equations can it solve?

It solves linear equations, where every variable appears only to the first power and is not multiplied by another variable or placed inside a function. Products such as x*y, powers such as x^2, divisions by a variable and functions such as sin(x) are reported as not linear. For a single quadratic, use the Quadratic Equation Solver.

### How are the variables recognized?

Every name that starts with a letter and is not a built-in constant or function becomes a variable, and they are listed in alphabetical order. pi, e, tau and phi are constants, so 2pi x = 1 has one variable x. Write x*y rather than xy, because xy is read as a single variable.

### Are the solutions exact?

When every coefficient is a rational number, including decimals such as 0.25, the elimination runs on exact fractions and shows results such as x = 3/2 together with the decimal. If coefficients involve irrational values such as sqrt(2) or pi, the solver switches to decimal arithmetic and says so in the method row.

### What does no solution mean?

The equations contradict each other, as with x + y = 1 and x + y = 2, which describe parallel lines. Elimination then produces a row that reads 0 = a nonzero number. The tool reports that the system has no solution.

### What does infinitely many solutions mean?

Some equations are dependent, so there are fewer independent equations than unknowns. The tool lists the free variables and expresses the other variables in terms of them, for example x = 3 - (1/2)z. Every choice of the free variables gives a valid solution.

### Which method does the solver use?

It reads the coefficient of every variable from each equation and runs Gauss-Jordan elimination on the augmented matrix. With exact fractions any nonzero pivot is used; in decimal mode the largest pivot is chosen for numerical stability. The rank of the matrix decides between one, none or infinitely many solutions.

### Can the system have more equations than unknowns?

Yes, an overdetermined system is solved as long as the equations are consistent, and redundant equations are simply eliminated. If they conflict, the result is no solution. The limits are 10 equations and 10 variables.

### Can I use functions and constants in coefficients?

Yes, coefficients may contain constant expressions such as sqrt(2) x + y = 3 or x / 4 = pi. Functions of a variable are not allowed, because they make the equation nonlinear. The whole input is limited to 2000 characters.

### How are decimal results rounded?

Decimals are rounded to 6 places by default and you can choose 0 to 15. Exact fraction results are shown in full next to their decimal value. Very small nonzero values are shown in scientific notation instead of rounding to zero.

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