System of Equations (2×2)
Solve two linear equations with the intersection point
About this calculator
The System of Equations (2×2) Calculator solves two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂ for x and y using Cramer's rule. It finds the exact intersection point, or tells you when the lines are parallel (no solution) or identical (infinitely many solutions), with a graph of both lines.
How to use the System of Equations (2×2) calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- x + y = 5 and 2x − y = 1 → x = 2, y = 3
- 3x + 2y = 1 and x − y = 1 → x = 0.6, y = −0.4
- x + y = 1 and 2x + 2y = 5 → no solution (parallel lines)
- x + y = 1 and 2x + 2y = 2 → infinitely many solutions (same line)
Frequently asked questions
How does the System of Equations (2×2) calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the System of Equations (2×2) calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.