Equation form: a·x + b = 0
Our free Linear Equation Calculator helps you solve linear equations and systems of equations step-by-step. Whether you’re working on a single-variable equation or a set of simultaneous equations, this tool gives you quick and accurate results.
Supports:
Single variable linear equations (ax + b = 0)
Two-variable simultaneous equations (ax + by = c)
Three-variable systems (ax + by + cz = d)
Linear equations are the foundation of algebra and mathematics. They appear in everyday problem-solving, from finance to physics.
This calculator is designed for:
✅ Students checking homework
✅ Teachers explaining step-by-step solutions
✅ Professionals needing quick equation solving
✅ Anyone solving systems of equations
Equation: ax + b = 0
Solution: x = -b / a
Equations:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Solution (Cramer’s Rule):
x = (c₁b₂ – c₂b₁) / (a₁b₂ – a₂b₁)
y = (a₁c₂ – a₂c₁) / (a₁b₂ – a₂b₁)
System:
a₁x + b₁y + c₁z = d₁
a₂x + b₂y + c₂z = d₂
a₃x + b₃y + c₃z = d₃
Solution via determinants (Cramer’s Rule).
Q: What is a linear equation?
A linear equation is an equation where the highest power of the variable is 1 (e.g., 2x + 3 = 7).
Q: Can this calculator solve systems of equations?
Yes ✅ — it can handle two-variable and three-variable systems.
Q: How does it solve simultaneous equations?
It uses algebraic methods like substitution, elimination, or determinants.
Q: What if there is no solution?
If equations are parallel, the calculator shows no solution.
Q: What if there are infinite solutions?
If equations are dependent (multiples of each other), the tool shows infinite solutions.