Systems

2×2 and 3×3, guaranteed to have one solution and to reach it without fractions.

equations.system · v1 · renderer math

1. -3x - 5y = -13 ; -x - 2y = -6 → x = -4, y = 5 2. x + 4y = 18 ; -2x - 7y = -33 → x = 6, y = 3 3. 5x - 4y = 4 ; 9x - 7y = 7 → x = 0, y = -1 4. 2x + y = 12 ; -x - y = -6 → x = 6, y = 0

entropy in

16 bytes

stream used

183 bytes

rejections

duration

540 µs

problems

Seed receipt

Class B · Public beacon

NIST Beacon pulse #1,939,957 — chained to every pulse before it, and signed.

Published openly — anyone can look this value up after the fact.

source: NIST Randomness Beacon
observed: 2026-09-13T18:43:00+00:00
latency: 112ms
mixed with: csprng — always

https://beacon.nist.gov/beacon/2.0/chain/2/pulse/1939957 ↗

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The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

Controls · from schema()

Size

How many

1 30

Solutions within ±

2 20

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from NIST Randomness Beacon.

seed token C6821QHVH73KRVM722M9FDQRH0

Re-render keeps this token. Generate replaces it. That is the whole idea.

Printable worksheet 20 problems · answers on page 2

The seed is printed in the footer, so the same sheet comes back from the same link — and a different seed is a different sheet.

This page and /api/v1/g/equations.system run the same code. There is no private endpoint.

Systems

Result

Measurements

Seed receipt

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