Simultaneous Equations Solver
Solve simultaneous equations — systems of two or more equations.
Finding values that satisfy several equations
Simultaneous equations are a set of equations that must all be true at once, and solving them means finding the values that satisfy every equation together. This solves a system of equations, finding the point where they all agree.
Enter your equations to solve the system.
What the solution means
Geometrically, two equations in two unknowns are two lines, and the solution is where they cross — the single point that lies on both. This picture explains the special cases: parallel lines never meet, so a system can have no solution, and two equations describing the same line meet everywhere, so it can have infinitely many. Simultaneous equations are how you solve real problems with several unknowns and several constraints — mixing two solutions to hit a target, splitting a total under two conditions, balancing supply and demand. The method scales to more equations and unknowns, and is the foundation of a huge amount of applied maths, all resting on the simple idea of finding where multiple conditions are satisfied together.
Common questions
What does solving simultaneous equations find?
The values that make all the equations true at once — geometrically, the point where the lines they describe cross.
Can a system have no solution?
Yes — if the equations describe parallel lines they never meet, giving no solution, and identical lines meet everywhere, giving infinitely many.
Is anything uploaded?
No. The calculation happens in your browser.