Formula Explanation
x = (c1b2 - c2b1) / (a1b2 - a2b1)
This calculator applies the formula x = (c1b2 - c2b1) / (a1b2 - a2b1). Enter each value with the matching unit, and AZCalculate updates the result instantly.
Mathematics
System of Equations Calculator
Use this system of equations calculator to calculate solve a 2x2 linear system a1x + b1y = c1 and a2x + b2y = c2.
system of equations2x2linear algebra
Calculator
Calculate instantly
b2 must be at least 0 .
Calculator Inputs
Choose what you want to calculate, enter realistic values, adjust units where shown, and use the scenario section for repeated-use planning.
Input and Formula Breakdown
This calculator applies the formula x = (c1b2 - c2b1) / (a1b2 - a2b1). Enter each value with the matching unit, and AZCalculate updates the result instantly.
a1
2
b1
1
c1
7
a2
1
b2
-1
c2
1
x
2.67
y
1.67
Scenario and Comparison
Current
2.67
Projected
32
Adjusted
2.93
Visual Comparison
Current result2.67
Projected usage32
Comparison scenario2.93
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Use Cases
- Solve algebra systems
- Check simultaneous equations
- Study matrices
Step-by-Step Explanation
- Step 1Enter the known values in the calculator fields.
- Step 2Keep the units consistent with the labels shown beside each input.
- Step 3Apply the formula: x = (c1b2 - c2b1) / (a1b2 - a2b1).
- Step 4Review the primary result and supporting values.
Example calculation
Example system of equations calculator
Given
- a1: 2
- b1: 1
- c1: 7
- a2: 1
- b2: -1
- c2: 1
Steps
- Use the values shown above.
- Apply x = (c1b2 - c2b1) / (a1b2 - a2b1).
Result
The calculator above shows the computed answer instantly from these example values.
Calculator guide
About this System of Equations Calculator
Solve a 2x2 linear system a1x + b1y = c1 and a2x + b2y = c2. This page includes an interactive calculator, concise formula notes, worked examples, FAQs, related calculators, and practical guidance you can revisit whenever needed.
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Calculator usage
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Most active date
2026-06-05
FAQ
System of Equations Calculator FAQs
How does the system of equations calculator work?+
It uses x = (c1b2 - c2b1) / (a1b2 - a2b1) and calculates the result from the values you enter.
Can I copy or print the result?+
Yes. AZCalculate calculator pages include copy, share, and print actions.
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