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Elimination Method Calculator.

Solve a two-equation linear system a₁x + b₁y = c₁ and a₂x + b₂y = c₂.

On-device calculationNo signup
01

Set your values

Results update as you type.

x: 3.2

x

0.000000
y: 2.2

y

0.000000
determinant: -5

determinant

0.000000

Results update automatically as you type.

Use Cases

Homework and exam practice

Check your work when solving systems of linear equations by elimination. Enter your coefficients and compare the step-by-step solution to your own.

Example: Verify that 2x + 3y = 6 and 4x - y = 5 gives x = 1.5, y = 1.

Quick solution for real-world linear problems

Use it to solve two-variable linear models, such as finding break-even points or mixing problems, when you have two linear equations.

Example: Solve for quantities when 5x + 2y = 100 and 3x + 4y = 120.

Frequently Asked Questions

What is the elimination method for solving linear systems?
The elimination method (also called addition method) solves a system of two linear equations by adding or subtracting the equations to eliminate one variable. You multiply one or both equations by constants so that the coefficients of one variable are opposites, then add to cancel that variable, solve for the other, and back-substitute.
How do I enter the coefficients in this calculator?
Enter the coefficients a₁, b₁, c₁ for the first equation (a₁x + b₁y = c₁) and a₂, b₂, c₂ for the second equation (a₂x + b₂y = c₂). Ensure you include the correct signs. For example, for 2x - 3y = 5, enter a₁=2, b₁=-3, c₁=5.
What if the system has no solution or infinite solutions?
If the equations are inconsistent (parallel lines), the calculator will indicate no solution. If they are dependent (same line), it will indicate infinite solutions. The elimination method will reveal these cases when the eliminated variable leaves a false or true statement.

Tips & Common Mistakes

Tips

  • Double-check the signs of your coefficients, especially negative values, to avoid errors.
  • If a variable is missing, enter 0 for its coefficient. For example, for 3x = 9, enter b₁=0.
  • Use the step-by-step solution to understand the elimination process, not just the final answer.
  • Ensure equations are in standard form (ax + by = c) before entering coefficients.

Common Mistakes to Avoid

  • Forgetting to multiply the constant term (c) when multiplying an equation to align coefficients.
  • Entering coefficients in the wrong order (e.g., swapping a and b).
  • Misreading the sign of a coefficient, such as entering 3 instead of -3 for a term like -3x.

Last updated: August 13, 2026