Linear Equation Solver
Solve linear equations and systems of equations (2x2). Step-by-step solutions shown.
About Equation Solver
Solve single variable equations like "3x + 5 = 14" or two simultaneous equations. Enter equations in natural form.
About this calculator
Solve a linear equation in one unknown, such as 3x + 5 = 14, or a pair of simultaneous equations, such as 2x + 3y = 8 and x − y = 1. Type the equations the way you would write them.
The solver isolates the variable step by step. For the 2×2 system it finds x and y, and tells you if the equations have no solution or infinitely many.
How to use it
- Choose Single Equation or 2×2 System.
- Type the equation or equations.
- Press Solve.
Method
For one equation, collect the x terms on one side and the numbers on the other, then divide: 3x + 5 = 14 → 3x = 9 → x = 3. For two equations, use substitution or elimination: from x − y = 1, x = 1 + y; then 2(1 + y) + 3y = 8 gives y = 1.2 and x = 2.2.
Worked example
Examples
| 3x + 5 = 14 | x = 3 |
| 2x + 3y = 8 and x − y = 1 | x = 2.2, y = 1.2 |
| x + y = 10 and x − y = 2 | x = 6, y = 4 |
Tips and common mistakes
- Check the solution by substituting back into the original equation.
- Do the same operation to both sides.
- If elimination makes everything cancel to 0 = 0, there are infinitely many solutions.
- If it gives 0 = 5, the system has no solution.
- Write multiplication clearly, for example 3x or 3*x.
Frequently asked questions
How do I solve 3x + 5 = 14?
Subtract 5 from both sides to get 3x = 9, then divide by 3.
What is a system of equations?
Two or more equations with the same unknowns that must hold together.
What is elimination?
Adding or subtracting equations to remove one variable.
What is substitution?
Solving one equation for a variable and putting it into the other.
What if there is no solution?
The lines are parallel and never meet.
Can it solve quadratics?
Use the Quadratic Equation Solver for those.