Math & Scientific
System of Equations Calculator
Solve two linear equations in x and y. The calculator reads their coefficients, checks the expression structure and uses a determinant calculation to find a unique solution when the equations can be distinguished at its numerical precision.
Enter both equations with an equals sign. Constant multiplication, division by nonzero constants and parentheses are supported; products of variable expressions, variable denominators and nonlinear functions are outside this tool’s scope.
About this calculator
The calculator solves a two-variable linear system using its coefficients and a determinant formula. For example, x+y=10 and x-y=4 give x=7 and y=3. Adding the equations by hand gives 2x=14, and substitution verifies both original equations. The displayed result is numerical rather than an exact symbolic proof.
How to use
- Type the first equation in x and y, for example 2x + y = 5.
- Type the second equation in x and y, for example x - y = 1.
- Press Calculate to solve the two equations together.
- Read the values of x and y that satisfy both equations.
Why use System of Equations Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Based on standard, well-established formulas.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it when working through problems
Use it when revising for exams
System of Equations in tutoring and teaching sessions
Use it for quick mental-math cross-checks
Use it for homework and assignment checks
System of Equations in competitive-exam practice
Technical notes
Expression validation propagates constant and x/y coefficients through the input operations. It rejects nonlinear products and variable denominators before solving.
Each coefficient row is normalized before the determinant check. Parallel, dependent or numerically indistinguishable near-parallel equations do not produce a unique result; this tool does not separately classify no-solution and infinitely-many-solution cases.
Calculation uses JavaScript finite-precision numbers and rounds the displayed solution. Check a candidate in both original equations, especially when coefficients differ greatly in size.
FAQ
What systems can this solve?
It solves a system of two linear equations in two unknowns, x and y, returning the single point where the two lines meet.
What if the lines are parallel?
Parallel or identical lines do not have one unique solution. The calculator also reports when equations are too nearly parallel to distinguish at its numerical precision; it does not separately classify inconsistent and dependent systems.
How should I write each equation?
Write each equation with an equals sign and use x and y, for example 3x + 2y = 12. Implicit multiplication like 2x is accepted.
Does the System of Equations Calculator send my data to a server?
No. The System of Equations Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
Solve x + y = 10 and x − y = 4: adding gives 2x = 14, x = 7, then y = 3.