Solve one-variable and two-variable linear equations step by step.
A linear equation is an algebraic equation where each term is either a constant or a product of a constant and a single variable, with no exponents greater than 1. The solution forms a straight line when graphed.
The Linear Equation Solver on Calculator Expert solves single-variable equations (ax + b = c) and systems of two-variable linear equations (ax + by = c and dx + ey = f) using substitution or elimination methods, with full step-by-step working.
| Equation | Solution | Type |
|---|---|---|
| x + 3 = 7 | x = 4 | 1-variable |
| 2x − 5 = 9 | x = 7 | 1-variable |
| x + y = 5, 2x − y = 1 | x=2, y=3 | 2-variable system |
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Method 1: Isolation Method: Move all variable terms to one side and constants to the other, then divide both sides by the coefficient of the variable to isolate x.
Method 2: Elimination Method: For two-variable systems, multiply equations to make one variable's coefficients equal in magnitude, then add or subtract to eliminate that variable.
For two-variable systems, if the determinant (a₁b₂−a₂b₁) equals zero, the system is either inconsistent (no solution) or dependent (infinite solutions). Single-variable equations require a ≠ 0.
Linear approximations are used in health to estimate body measurements from surrogate measures. For example, predicting height from arm span uses a linear equation derived from population regression data, which is then used in Ponderal Index calculations for patients who cannot stand.
Linear equations model cost-revenue break-even analysis, speed-distance-time problems, temperature conversion, currency exchange, and chemical equation balancing.