Introduction
Where do a set of linear constraints — a budget limit, a resource cap, a supply-demand balance — actually agree with each other, if anywhere? SolveSystemOfEquations solves a system given its coefficient matrix and constants vector, checks the determinant to flag singular (unsolvable or redundant) systems, and for two-variable systems plots each equation as a line so you can see the solution as the point where they intersect.
Teaching Note
Solving and plotting systems of equations is essential for:
- Finding intersection points of multiple linear constraints in business models
- Analyzing market equilibrium in supply and demand economics
- Determining unique solutions for multi-variable experimental datasets
- Identifying redundant or inconsistent constraints in optimization problems
- Modeling resource allocation and balanced production planning
- Visualizing decision boundaries for simple linear classification tasks
- Assessing system stability through determinant analysis
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
coefficientsrequired | | — | A matrix containing the coefficients of the variables in the system. Expected as a nested list or a square 2D numpy.ndarray. |
constants | | None | A 1D array or list representing the constants on the right-hand side of the equations. If None, it defaults to a zero vector (homogeneous system). |
show_plot | | True | Whether to generate a 2D visualization of the equations. Only applicable for systems with exactly two variables. Defaults to True. |
plot_boundary | | 10 | The range (from -value to +value) used for the x-axis in the plot. Defaults to 10. |
Returns
None — the function prints the determinant and solution to the console and displays a plot if requested and applicable.
Example
python
from analysistoolbox.linear_algebra import SolveSystemOfEquations
# Solve a 2x2 system: 2x + 1y = 10 and 1x - 1y = 2
coeffs = [[2, 1], [1, -1]]
consts = [10, 2]
SolveSystemOfEquations(coeffs, consts)