Nirmion
Help Find a tool

ALGEBRA / TWO LINEAR EQUATIONS

Simultaneous Equations Calculator

Solve two equations in x and y using their six coefficients, with determinant-based detection of non-unique systems.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Equation 1

Equation 2

Preparing the calculator...

Use boundary

Calculation path

Cramer’s rule divides two coefficient-replacement determinants by the non-zero coefficient determinant.

Calculation path

x = (c1b2 - c2b1) / determinant; y = (a1c2 - a2c1) / determinant.

What you provide

What you provide

  • First equation x coefficient: Coefficient a1 in a1x + b1y = c1.
  • First equation y coefficient: Coefficient b1 in a1x + b1y = c1.
  • First equation constant: Right-side constant c1.
  • Second equation x coefficient: Coefficient a2 in a2x + b2y = c2.
  • Second equation y coefficient: Coefficient b2 in a2x + b2y = c2.
  • Second equation constant: Right-side constant c2.

What you receive

What you receive

  • Unique x and y solution
  • Individual numeric coordinates
  • Coefficient determinant

Use boundary

Choose the maximum decimal places shown. This does not increase source accuracy.

A zero determinant can mean no solution or infinitely many solutions; this calculator reports only that a unique solution is unavailable.

Results are educational math aids. Check notation, units, rounding, assumptions, and required precision before using an answer in graded, engineering, financial, or safety-critical work.

Continue converting

Linear Equation CalculatorSlope CalculatorQuadratic Equation Calculator