A consistent, independent system
- Input
- 2x + y = 5 x - y = 1
- Expected output
- x = 2, y = 1
The two lines cross at a single point, there is exactly one solution.
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system of linear equations
A system of linear equations is a set of two or more equations that share the same unknowns, and "solving the system" means finding the values of those unknowns that satisfy every equation at once. This page opens the calculator with a sample 2x2 system already loaded, ready for you to swap in your own.
The two lines cross at a single point, there is exactly one solution.
The second equation is the first one multiplied by 2, so the two lines coincide: infinitely many solutions.
One equation per line, with an equals sign separating the two sides, for example "2x + 3y = 8" or "x - y = -1". The calculator accepts an implicit coefficient ("x" means the same as "1x"), a negative sign, unknowns with any name, a variable appearing on both sides of the equals sign ("2x + 1 = x + 4"), and a variable that simply doesn't appear in one of the equations, it is treated as a zero coefficient automatically.
Up to 6 unknowns, with any number of equations (including systems with more equations than unknowns, or fewer).
Just "x" works fine, the coefficient 1 is implicit, the same way you'd write it by hand.
calculadoraSistemaEquacoes.classificationDesc.determined
Matrix representation
[ 2 1 ] [ 1 -1 ]
[ x ] [ y ]
[ 5 ] [ 1 ]
[ 2 1 | 5 ] [ 1 -1 | 1 ]
[ 1 0 | 2 ] [ 0 1 | 1 ]
[ 1 1/2 | 5/2 ] [ 1 -1 | 1 ]
[ 1 1/2 | 5/2 ] [ 0 -3/2 | -3/2 ]
[ 1 1/2 | 5/2 ] [ 0 1 | 1 ]
[ 1 0 | 2 ] [ 0 1 | 1 ]
Substitution check
Just need to invert, multiply or transpose a matrix, without solving a system? Use the matrix calculator
Everything runs in your browser: the equations you type and the system's calculation never touch a server.