Exact two-variable elimination

System of Equations Solver

Solve two linear equations together, inspect the elimination and substitution, and accept an answer only after an independent solver confirms the complete solution set.

Open the solver See the boundary

Enter both equations in one line

Separate the equations with one semicolon. The solver reduces both rows with exact rational arithmetic, eliminates one variable, substitutes back, and checks the ordered pair against both original equations.

Example input

egin{cases}2x+y=7\x-y=2\end{cases}

2x+y=7; x-y=2

x=3,\quad y=1

Current limitations

Exactly two equations and two single-letter variables.
First-degree expressions with exact rational coefficients.
No nonlinear systems, three-variable systems, functions, or variables in denominators.
Unique, inconsistent, and dependent systems are distinguished explicitly.

Questions

System of equations solver FAQ

How do I enter a system?

Enter exactly two equations separated by a semicolon, such as 2x+y=7; x-y=2.

What outcomes can the solver identify?

It verifies a unique ordered pair, no solution for inconsistent parallel equations, or infinitely many solutions for dependent equations.

Which systems are supported?

The current boundary is two linear equations in exactly two single-letter variables, with exact rational coefficients and no variables in denominators.