EquateIt Simultaneous Equations on CAS
Solve linear and non-linear systems on the TI-Nspire — and answer the 'find the value(s) of k' questions that trip students up — in one command.
The question type that costs marks
Most simultaneous-equation marks in VCE Mathematical Methods aren't lost on a straight 2×2 system — the
calculator's built-in solve() handles those. They're lost on the parameter
version: "find the value(s) of k for which the system has a unique solution / infinitely many
solutions / no solution." That requires reasoning about the determinant, and under exam time pressure it's
easy to set up wrong.
The EquateIt linesolve UDF does the classification and shows the determinant working, so you can
check your by-hand answer instantly. For graphical or non-linear systems, intersects and
intersectsd return the intersection points (the latter restricted to a domain), and
invints handles intersections involving a parameter. ca column-augments a system into
matrix form when a question wants the matrix method.
These are part of the free EquateIt CAS UDF library. If simultaneous-equation parameter questions are a recurring weak spot, a VCE Methods tutor can drill the exact set-out examiners reward.
The functions you'll use
linesolve(eq1, eq2) Unique/None/Infinite solutions
intersects(f1, f2, x) Points of intersection
intersectsd(f1, f2, x, lo, hi) Intersections in restricted domain
invints(f, n) Inverse intersections with parameter k
ca(ans, vars) Column augment to matrix form
Store it once, use it in the exam
- 1
Open the Program Editor
On a Calculator page, press Menu → Functions & Programs → Program Editor → New. Name the program after the function — for example, linesolve — and choose Type: Function or Program as the pack specifies.
Screenshot: open the program editor (coming soon) - 2
Paste the function from the EquateIt pack
Open the downloaded Functions pack, copy the linesolve (and intersects) definition, and paste it between Prgm and EndPrgm. Mark it as a public library function (LibPub) so you can call it from any document.
Screenshot: paste the function from the equateit pack (coming soon) - 3
Save it into MyLib
Save the document into the MyLib folder on your TI-Nspire. Anything stored in MyLib becomes a reusable library available across every exam document.
Screenshot: save it into mylib (coming soon) - 4
Refresh Libraries
Press Menu → Refresh Libraries (or restart the document). The new command now registers — type the first few letters and it appears in the catalog.
Screenshot: refresh libraries (coming soon) - 5
Call it in the exam
On any Calculator page type linesolve(eq1, eq2) — for parameter problems — or intersects(f1, f2, x) for two curves. The output classifies the solution (unique / infinite / none) or returns the intersection points, with the working shown.
Screenshot: call it in the exam (coming soon) - 6
Write up the required steps
The UDF confirms the answer in seconds, but VCAA still awards method marks for the set-out. Transcribe the determinant condition or the simultaneous-equation steps onto your paper — the calculator just removes the arithmetic risk.
Screenshot: write up the required steps (coming soon)
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