How does the System of Equations Solver work?

2×2 system: use Cramer's rule or elimination Then: Determinant det = a₁b₂ − a₂b₁ Then: x = (c₁b₂ − c₂b₁)/det Then: y = (a₁c₂ − a₂c₁)/det.

Can you give an example of how to use the System of Equations Solver?

Example: Input 2x+3y=13, 4x−y=5 gives a result of x=2, y=3.

Is the System of Equations Solver free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the System of Equations Solver?

Our System of Equations Solver uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Hisabati

System of Equations Solver

2×2 Linear System Solver

2x + 3y = 13
4x + -1y = 5

a₁

b₁

c₁ (RHS)

a₂

b₂

c₂ (RHS)

✓Solution

2.0000

3.0000

det

-14.0000

A system of linear equations is a set of two or more equations with the same variables. The solution is the point(s) where all equations are satisfied simultaneously.

Symbol	Name	Unit	Description
A	coefficient matrix (m × n)	—	—
x	variable vector (n × 1)	—	—
b	constant vector (m × 1)	—	—

det	Solution type	Geometric interpretation
≠0	Unique solution	Lines intersect at one point
=0, consistent	Infinite solutions	Lines are identical
=0, inconsistent	No solution	Lines are parallel

References

›Systems of equations — Khan Academy

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System of Equations Solver

2×2 Linear System Solver

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2×2 Linear System Solver

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