How to Use the Algebra Calculator
Use this calculator for one-variable linear or quadratic equations, or for systems of 2 or 3 linear equations. Select a mode, enter the equation or equations, and choose Solve to see the result and working steps.
- Select Linear equation, Quadratic equation, or System of equations.
- For a system, select 2 variables (x, y) or 3 variables (x, y, z). Changing this choice rebuilds the equation fields.
- Enter the equation or equations, then click Solve.
Choose an Equation Type
Use Linear equation for degree-1 equations in x. Use Quadratic equation for degree-2 equations in x. Use System of equations for 2 or 3 linear equations, then choose the matching variable count.
Enter a Supported Equation
Enter numbers, including decimal numbers, the supported variables, + - * / ^, and parentheses. Implicit multiplication is accepted, so you can enter 2x, 3(x + 1), or x(x + 2). Enter fractions with division, such as x/3 or 1/2 x.
- Use
xin linear and quadratic modes. Usexandy, orx,y, andz, in system mode. - Use non-negative whole-number exponents from
0through6. Variables cannot be used in denominators or exponents. - Include exactly one
=sign in each equation and keep it within200characters. - Linear mode accepts degree 1, quadratic mode requires a degree-2 term in
x, and system equations must have total degree at most 1. Squared terms and products such asx^2orxyare not supported in systems. - The quadratic solving path checks coefficients and the discriminant against
1,000,000. This is not a stated uniform bound for every mode.
The calculator rejects higher-degree polynomials, inequalities, trigonometric, logarithmic, and exponential expressions, as well as systems larger than 3 equations. Unsupported symbols, unbalanced parentheses, variables in denominators or exponents, and invalid equation structures also produce errors.
Solve and Read the Result
For a linear equation, the calculator rearranges the expression to ax + b = 0 and isolates x. It can report a value, no solution, or infinitely many solutions.
For a quadratic, it calculates D = b^2 - 4ac. A positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives two complex roots. Irrational roots include a simplified radical and a decimal approximation.
For a system, elimination uses exact-fraction arithmetic and displays row operations. A consistent system can produce a solution; an inconsistent system has no solution; and a dependent system has infinitely many solutions.
Copy, Download, or Reset Results
- Choose Copy result to copy the displayed result when clipboard access succeeds. If it fails, the page shows Could not copy - select and copy manually.
- Choose Download result (.txt) to download the result as
algebra-calculator-result.txt. - Choose Reset to clear the inputs, restore Linear equation and 2 variables (x, y), and hide the result.
Limitations and Privacy Scope
The calculator parses and calculates the equation locally in your browser. The calculator code does not send the equation for calculation. This statement applies to the calculator functionality; the page also loads its own analytics scripts.
Frequently Asked Questions
What kinds of equations can this calculator solve?
It solves degree-1 equations in x, degree-2 equations in x, and systems of 2 or 3 linear equations in x, y, and optionally z. It does not solve higher-degree polynomials, inequalities, or equations using trigonometric, logarithmic, or exponential functions.
What notation does the calculator accept?
Use numbers, including decimal numbers, the supported variables, + - * / ^, and parentheses. Implicit multiplication such as 2x, 3(x+1), and x(x+2) is accepted. Fractions can be entered as division, such as 1/2 x.
How does it show the discriminant and roots for a quadratic?
It calculates D = b^2 - 4ac. If D is positive, it shows two real roots; if D is zero, one repeated root; and if D is negative, two complex roots in a + bi form.
How does it solve a system of equations?
It uses elimination with exact fractions, shows the row operations, and reports each variable when the system has a unique solution. It identifies inconsistent systems as having no solution and dependent systems as having infinitely many solutions.
Does the calculator execute my input as code?
No. A fixed expression grammar parses numbers, the supported variables, the listed operators, and parentheses. It does not evaluate arbitrary code, and unsupported input produces an error.