Cramer's Rule Solver
Solve systems of linear equations using determinants and Cramer's Rule. Get instant step-by-step solutions — completely free, no signup required.
Free Cramer's Rule Solver Calculator
Enter your problem below to get an instant step-by-step solution.
About Cramer's Rule Solver
Solve systems of linear equations using determinants and Cramer's Rule. Linear algebra and matrix operations are foundational to computer graphics, machine learning, and solving systems of equations. Understanding matrix manipulations is critical for advanced mathematics.
Our Cramer's Rule Solver calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any cramer's rule solver expression and receive a complete, verified solution with every step shown.
Cramer's Rule Solver Formula
xᵢ = det(Aᵢ) / det(A)
Cramer’s rule solves a square linear system using determinants. Replace column i of the coefficient matrix with the constants to get Aᵢ; the i-th variable is det(Aᵢ) divided by det(A). It only works when det(A) ≠ 0.
Worked Example
Solve 2x + 3y = 8, x − y = −1
- det A = 2·(−1) − 3·1 = −5
- Aₓ = [[8, 3], [−1, −1]] → det = −8 + 3 = −5
- Aᵧ = [[2, 8], [1, −1]] → det = −2 − 8 = −10
- x = −5 / −5 = 1; y = −10 / −5 = 2
Answer: x = 1, y = 2
Common Mistakes to Avoid
- Replacing a row instead of a column with the constants.
- Using the rule when det(A) = 0.
- Using it on large systems, where elimination is far less work.
How to Use the Cramer's Rule Solver Calculator
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Input your matrix or vector values for the Cramer's Rule Solver problem
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Cramer's Rule Solver formula?
xᵢ = det(Aᵢ) / det(A). Cramer’s rule solves a square linear system using determinants. Replace column i of the coefficient matrix with the constants to get Aᵢ; the i-th variable is det(Aᵢ) divided by det(A). It only works when det(A) ≠ 0.
Can you show a worked Cramer's Rule Solver example?
Solve 2x + 3y = 8, x − y = −1: det A = 2·(−1) − 3·1 = −5; Aₓ = [[8, 3], [−1, −1]] → det = −8 + 3 = −5; Aᵧ = [[2, 8], [1, −1]] → det = −2 − 8 = −10; x = −5 / −5 = 1; y = −10 / −5 = 2. Answer: x = 1, y = 2.
Is this Cramer's Rule Solver calculator free to use?
Yes — the Cramer's Rule Solver calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Cramer's Rule Solver homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.