Steps
- Pick one of the example inputs or enter your own values.
- Use Solve to generate the direct answer and the conversion steps.
- Copy the result or share the URL with the query string intact.
Free math tool
Systems Of Equations Solver
Solve a 2x2 linear system in x and y, show the determinant-based reasoning, and identify parallel or identical lines.
Ready
Enter values to get the answer.
This page keeps the calculation direct: answer first, then steps, then explanation and examples.
Why it works
A system solution is the point where both equations are true at once. For two linear equations, that means finding where the two lines intersect or recognizing when they are parallel or identical.
Common mistakes
- Comparing only coefficients and forgetting to compare constants too.
- Solving each equation separately instead of solving them together.
- Missing that proportional equations can mean no solution or infinitely many solutions depending on the constants.
Worked examples
The intersection point is (3, 2).
The lines are parallel, so there is no solution.
Practice
- x + 2y = 8 and x - y = 2
- 2x + y = 7 and 4x + 2y = 14
- x + y = 3 and 2x + 2y = 10
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