What is the Simultaneous Equations Solver?
The simultaneous equations solver is a free online tool that helps you work out simultaneous equations solver quickly and accurately. It uses the standard formula Solve a1x+b1y=c1 and a2x+b2y=c2 by Cramer's rule and shows the result instantly as you type, along with a full breakdown so you can see exactly how the answer was reached.
How to use this calculator
- Enter the coefficients of both equations.
- See x and y.
Formula used
Solve a1x+b1y=c1 and a2x+b2y=c2 by Cramer's ruleExplanation of each input
- a1 โ the a1 used in the calculation.
- b1 โ the b1 used in the calculation.
- c1 โ the c1 used in the calculation.
- a2 โ the a2 used in the calculation.
- b2 โ the b2 used in the calculation.
- c2 โ the c2 used in the calculation.
Understanding your result
- x โ the calculated x.
- y โ the calculated y.
Step-by-step calculation
For the example values x+y=10; 2x-y=5:
- Apply the formula:
Solve a1x+b1y=c1 and a2x+b2y=c2 by Cramer's rule - Substitute the values: Cramer
- Result: x=5, y=5
Worked example
| Inputs | x+y=10; 2x-y=5 |
|---|---|
| Working | Cramer |
| Result | x=5, y=5 |
Benefits and practical uses
This calculator saves you time and reduces errors when you need simultaneous equations solver. It is useful for students, professionals and anyone who wants a fast, reliable answer without manual calculation. Results update instantly, work in your browser and can be copied or shared in one click.
Assumptions and limitations
- Non-zero determinant.
Frequently asked questions
What if there is no solution?
If the lines are parallel the determinant is zero and there is no unique solution.