Calculator
Result
Answer will appear hereEnter the values above and press Calculate to see the answer, step-by-step solution, and formula used.
How the result is calculated
\(x = \dfrac{D_{x}}{D},\; y = \dfrac{D_{y}}{D}\)
System of Linear Equations Calculator
Use this calculator to calculate system of linear equations using a clear formula and simple inputs.
Explanation
What this calculator does
System of Linear Equations Calculator helps you calculate the result using clear inputs, a formula, and practical examples.
How LearnLinx Calculates This Result
Formula
\(x = \dfrac{D_{x}}{D},\; y = \dfrac{D_{y}}{D}\)
Enter your values and press Calculate to see each computation step with your numbers plugged into this formula.
Example
Enter your values, calculate the result, and review the formula used for the answer.
When to use it
Use it when you need a quick result for study, planning, documentation, or checking a manual calculation.
Common mistakes
- Entering coefficients in the wrong order for x, y, and z.
- Treating a zero determinant as a normal unique solution.
- Mixing a 2×2 coefficient set with a 3×3 equation layout.
Frequently asked questions
How do I enter my equations?
Choose 2x2 or 3x3, then enter each coefficient in its own box. For 2x2, fill a₁, b₁, c₁ and a₂, b₂, c₂ for a₁x + b₁y = c₁ and a₂x + b₂y = c₂. For 3x3, also enter the z coefficients and a third equation.
What formula does the System of Linear Equations Calculator use?
It depends on the method you select. Substitution isolates one variable and substitutes. Elimination uses row operations to remove variables. Matrix inverse uses \( X = A^{-1}B \). Cramer's rule uses \( x = D_{x}/D \), \( y = D_{y}/D \) (and \( z = D_{z}/D \) for 3x3).
What if the determinant is zero?
When det(A) = 0 the system has no unique solution. If the equations are dependent there are infinitely many solutions; if they contradict each other there is no solution.
Is the System of Linear Equations Calculator free to use?
Yes. All LearnLinx calculators are completely free with no signup required. Signing in is optional and only adds a 60-day history of your calculations.