Math Tool✨ New Release
Linear Equation Calculator
Solve single variable linear equations (ax + b = c) and systems of two linear equations in two variables (ax + by = c, dx + ey = f) using algebraic steps.
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Interactive Linear Equation Calculator Workspace
Solved Variable Outputx = 3
Step-by-Step Solving Breakdown
Equation: (2)x + (5) = 11
Step 1: Subtract 5 from both sides:
(2)x = 11 - (5)
(2)x = 6
Step 2: Divide both sides by coefficient a = 2:
x = 6 / 2 = 3.0000
Mathematical Formula & Variables
Equation Model
x = (c - b)/a | x = (ce - bf)/(ae - bd), y = (af - cd)/(ae - bd)Single variable equations are solved by isolating x. Systems of two variables are solved via Cramer's rule using 2x2 determinants.
Variable Definitions
| Symbol | Description |
|---|---|
| a, b, c | Coefficients and constants for the linear equations |
| d, e, f | Coefficients and constants for the second equation in systems |
| x, y | The independent variables being solved |
How to Use the Linear Equation Calculator
- Select between "Single Variable" or "System of 2 Equations" mode.
- Enter the numerical coefficients in the designated inputs.
- Click calculate to reveal the intermediate elimination or isolation steps and final coordinates.
Practical Example Calculation
Scenario Context: Solving the 2-variable system: 2x + 3y = 8 and 4x - y = 2.
Step 1: Determine the main determinant D = (2 × -1) - (3 × 4) = -2 - 12 = -14.
Step 2: Determine Dx = (8 × -1) - (3 × 2) = -8 - 6 = -14.
Step 3: Determine Dy = (2 × 2) - (8 × 4) = 4 - 32 = -28.
Step 4: Solve for x = Dx / D = -14 / -14 = 1.
Step 5: Solve for y = Dy / D = -28 / -14 = 2.
The solution is x = 1, y = 2.
Frequently Asked Questions
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