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Linear Equations and Systems

Install and import#

bash
npm install fintech-algorithms
ts
import { linearEquationsAndSystems } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/linear-equations-and-systems";

Signature#

linearEquationsAndSystems(input)

Solves the two-equation system a*x + b*y = c and d*x + e*y = f by Cramer's rule, returning the solution and the determinant that decides whether one exists.

Parameters#

NameTypeNotes
inputD00InputA plain object. Every F01 topic first reads values, which must be a non-empty array of finite numbers, and validates it before any per-topic branch runs. This topic then reads the six coefficients a, b, c, d, e and f, each coerced with Number; values is demanded but not used by this calculation.

Returns#

{ x: number; y: number; determinant: number }

determinant is a*e - b*d. x is (c*e - b*f) over that determinant and y is (a*f - c*d) over it.

Errors#

  • When input is not a plain object — throws TypeError
  • When values is missing, empty, or not an array — throws RangeError
  • When values contains a value that is not a finite number — throws RangeError
  • When the determinant a*e - b*d is zero, so the system has no unique solution — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input
{
  "values": [1, 2, 3, 4, 5],
  "startingCash": 1000,
  "inflows": 250,
  "outflows": 120,
  "slope": 2,
  "intercept": 1,
  "part": 25,
  "whole": 200,
  "elapsed": 5,
  "old": 4.5,
  "new": 4.75,
  "base": 16,
  "exponent": 0.5,
  "a": 2
}

Showing 14 of 28 fields.

Call#

linearEquationsAndSystems(input)

Returns#

object with 2 fields: x, y

{
  "x": 3,
  "y": 1
}

Diagrams#

Linear Equations and Systems — concept anatomy
Linear Equations and Systems — lesson map
Linear Equations and Systems — mistake contrast

Calculation flow#

Linear Equations and Systems — four-part map 
flowchart LR
    A["Name the input"] --> B["Apply: a×x + b×y = c and d×x + e×y = f"]
    B --> C["Check units and boundary"]
    C --> D["Explain the output"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

  • NIST/SEMATECH e-Handbook of Statistical Methods — NIST/SEMATECH
  • Author-derived and synthetic boundary

The rest of the Mathematical Language and Quantitative Reasoning family#