Calculator For Systems Of Equations

System of Equations:

\[ \begin{cases} ax + by = c \\ dx + ey = f \end{cases} \]

Coefficient a:

Coefficient b:

Constant c:

Coefficient d:

Coefficient e:

Constant f:

Solution:

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1. What Is A System Of Equations?

A system of equations is a set of two or more equations with the same variables. This calculator solves systems of two linear equations with two variables (x and y) using the elimination method.

2. How Does The Calculator Work?

The calculator uses the following method:

\[ \begin{cases} ax + by = c \\ dx + ey = f \end{cases} \]

Where:

\( a, b, d, e \) — Coefficients of the variables
\( c, f \) — Constants
\( x, y \) — Variables to solve for

Method: The calculator computes the determinant (\( det = ae - bd \)) to determine if the system has a unique solution, no solution, or infinite solutions.

3. Understanding The Results

Unique Solution: When determinant is non-zero, the system has exactly one solution.
No Solution: When lines are parallel (inconsistent system).
Infinite Solutions: When equations represent the same line (dependent system).

4. Using The Calculator

Tips: Enter all six coefficients (a, b, c, d, e, f) as real numbers. The calculator will handle both integer and decimal inputs.

5. Frequently Asked Questions (FAQ)

Q1: What if I get "No solution"?
A: This means the equations represent parallel lines that never intersect, so there's no (x,y) that satisfies both equations.

Q2: What if I get "Infinite solutions"?
A: This means both equations represent the same line, so every point on the line is a solution.

Q3: Can this solve nonlinear systems?
A: No, this calculator only solves linear systems. Nonlinear systems require different methods.

Q4: What's the maximum size system this can solve?
A: This calculator is designed for 2×2 systems (two equations, two variables).

Q5: How precise are the solutions?
A: Solutions are rounded to 4 decimal places for readability.