My 8th-grade daughter is working on syst
Question
My 8th-grade daughter is working on systems of equations tonight.
In the problem:
Equation 1: 2x + 3y = 12
Equation 2: 2x - 5y = -4
She subtracted Equation 2 from Equation 1 to eliminate x, but for the y term she calculated 3y - (-5y) as -2y (forgetting that subtracting a negative is adding).
Could you help us:
- File this exact mistake into a single 5-line card (Prompt, Wrong, Fix/Parallel, Tag, Cause) without dumping generic math lectures.
- Provide one clean changed-number parallel item in the Fix line.
- Explain the [1, 3, 7, 14, 30] spaced repetition review schedule for when this card falls due.
Answer
That file was not generated this turn — the draft above is what I have. yours is the 26th and shows up tomorrow first.
Card #26 — systems-of-equations, sign-of-subtraction (id `e1ad200beadf9d93`, first due 2026-09-20)
| line | content |
|---|---|
| Prompt | Solve the system `2x + 3y = 12` and `2x − 5y = −4` by subtracting Eq2 from Eq1. Compute the y-term: `3y − (−5y)`. |
| Wrong | `3y − (−5y) = −2y` — treated "minus a negative" as another minus, so the y-terms combined the wrong way. |
| ight | Subtracting a negative is adding: `3y − (−5y) = 3y + 5y = 8y`, giving `8y = 16 → y = 2`. |
| Parallel (same type, new numbers) | `6x + 4y = 18` and `6x − 3y = −3`. Subtract Eq2 from Eq1 → y-term is `4y − (−3y) = 7y`; `7y = 21 → y = 3`, then `x = 1`. |
| Tag / Cause | `systems-of-equations, sign-of-subtraction` / *leave cause blank for now* — same-shape card can sit in the `distribute-negative` cluster (id `d468c36e…` and the four siblings on `−3(2x−5)` etc.) if you want to fold it in. |
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The [1, 3, 7, 14, 30] ladder
This is the spaced-repetition rhythm baked into the card, not a study schedule you set. A new card starts at +1 day (yours is due tomorrow, 2026-09-20). When she reviews it:
- Pass → next gap steps up the ladder: 1 → 3 → 7 → 14 → 30 days. After the +30 review she owns the card.
- Fail → gap resets to +1 day (tomorrow again), and she re-climbs.
- Skip / no review → the card stays parked at its current step until it's answered.
So tomorrow night the system will surface this card (and any others that fall due — there are 25 already waiting). She tries from memory first, you mark pass/fail, the script picks the next gap. If you want me to set a 7 pm daily nudge that surfaces whatever's due that day, say the word and I'll wire it.