Linear Equation Solver Formula
Understand the math behind the linear equation solver. Each variable explained with a worked example.
Formulas Used
X
x = a != 0 ? (c - b) / a : 0Y Intercept
y_intercept = bVariables
| Variable | Description | Default |
|---|---|---|
a | Coefficient a | 3 |
b | Constant b | 7 |
c | Equals c | 22 |
How It Works
How to Solve a Linear Equation
Formula
Given ax + b = c, solve for x:
x = (c - b) / a
1. Subtract b from both sides: ax = c - b 2. Divide both sides by a: x = (c - b) / a
This works for any linear equation with a single unknown, as long as a is not zero.
Worked Example
Solve 3x + 7 = 22.
- 013x + 7 = 22
- 023x = 22 - 7 = 15
- 03x = 15 / 3 = 5
Frequently Asked Questions
What is a linear equation?
A linear equation is an equation where the variable appears only to the first power (no squares, cubes, etc.). Its graph is a straight line.
What happens if a equals zero?
If a = 0, the equation becomes b = c, which is either always true (if b = c) or has no solution (if b ≠ c). There is no variable to solve for.
Can a linear equation have more than one solution?
A standard linear equation in one variable has exactly one solution (when a ≠ 0). Systems of equations can have zero, one, or infinitely many solutions.
Learn More
Guide
How to Graph Linear Equations
Learn how to graph linear equations using slope-intercept form, point-slope form, and two-point methods. Step-by-step guide with examples.
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