System of Equations Solver
Type two, three, or four linear equations and get the exact answer as fractions, not rounded decimals. You also get a graph of the lines, every elimination step, and a check that plugs the answer back in.
Solving a system by hand isn’t hard. It’s long, and one dropped minus sign ruins the answer. Type your equations the way they appear in the textbook. The solver moves every term to the right place, clears any fractions, and works through elimination one step at a time, so you can check your own work line by line. It also tells you when a system has no solution or infinitely many, and explains why.
Write 3x or 3*x, fractions as 1/2x or x/2, and decimals as 0.5x. Brackets work too, like 2(x + 3) = y, and terms can be on either side of the equals sign.
How the solver works, and when to use substitution instead
- Elimination, done the way you’d do it by hand. The solver multiplies two equations by whole numbers so that one variable cancels, and never divides until the last step. That keeps every intermediate line in whole numbers, just like the textbook method. Each step names the equations it combined, for example
3 × (2) − 2 × (1). - Why the answer is a fraction. The arithmetic is exact, so
12/7stays12/7and doesn’t become 1.714. A rounded decimal won’t pass the check, and teachers usually want the fraction anyway. - No solution vs. infinitely many. If elimination ends in a false statement like
0 = 1, the equations contradict each other. With two variables, that means parallel lines. If it ends in0 = 0, one equation repeats another, so the variable left over can be any number. The solver writes the other variables in terms of it. - Substitution. If one equation already reads
y = …, substitution is often quicker on paper. You’ll get the same answer either way, and the check section confirms it. - Cramer’s rule appears under the check for 2×2 and 3×3 systems with one solution, in case your class is covering determinants.
Everything runs in your browser. Your equations are saved on this device only.