Sistema Linear — Calculadora Online Grátis
Solve single and system of linear equations with step-by-step solution
The Linear Equation Solver handles both single-variable linear equations and systems of two or three linear equations simultaneously. It shows step-by-step elimination or substitution, making it a practical study companion for algebra students. Engineers and scientists also use it to solve balance equations and constraint systems quickly.
Frequently Asked Questions
Sobre Esta Calculadora
A linear equation is one where every variable appears to the first power, with no products between variables. A single linear equation in one variable (e.g., 3x + 7 = 22) has exactly one solution found by isolation. A system of two linear equations in two variables can be solved by substitution or elimination, producing the coordinates where two lines intersect.
This solver handles single-variable equations, two-equation/two-variable systems, and three-equation/three-variable systems. For systems, it uses elimination (subtracting multiples of equations to cancel variables) and shows each algebraic step. When a system has no solution (parallel lines) or infinitely many (coincident lines), the calculator detects and reports that.
Linear equations model countless real-world relationships: budgeting constraints (linear programming), mixture problems, rate and distance problems, electrical circuit analysis (Kirchhoff's laws), and supply-demand equilibrium in economics.
Substituições e linhas de cálculos.
Exemplo Resolvido
Solving a 2×2 system: 3x + 2y = 16 and x − y = 2
Entradas:
- Equation 1: 3x + 2y = 16
- Equation 2: x − y = 2
Passo a Passo:
- From Equation 2: x = y + 2
- Substitute into Equation 1: 3(y + 2) + 2y = 16
- 3y + 6 + 2y = 16
- 5y = 10
- y = 2
- Substitute y = 2 back: x = 2 + 2 = 4
- Verify: 3(4) + 2(2) = 12 + 4 = 16 ✓ and 4 − 2 = 2 ✓