Substitution and elimination work, but on a timed test they're slow and error-prone. The built-in Desmos calculator turns every two-equation system into a picture: two lines, one crossing, done.
The move: Type both equations, tap the crossing.
Why it works: The solution to a system is the one (x, y) pair that satisfies both equations — and that's exactly what an intersection point is.
The pattern
- Type equation 1 exactly
- Type equation 2 exactly
- Tap the crossing, answer what’s asked
Worked example: If 2x + 3y = 12 and x − y = 1, what is x + y?
- Type the first equation EXACTLY as written — Desmos doesn’t need y= form.
2x+3y=12 - Second equation. Watch the two lines appear.
x-y=1 - Tap where they cross: (3, 2). So x + y = 5.
Worked example 2: If 3x + 2y = 7 and x = y + 4, what is the value of xy?
- First equation in, exactly as written.
3x+2y=7 - The second one isn’t solved in standard form? Desmos does not care.
x=y+4 - Intersection: (3, −1). The question wants the PRODUCT: 3 · (−1) = −3.
Remember it on test day
Where they meet. That's the whole cue — say it when you see this question type and the steps follow.
When this isn't the move
Systems with three variables, or symbolic answers in terms of a and b, still need algebra — the calculator graphs two-variable equations.
Drill it until it's reflex
This move is one of Desvantage's 18 training modules: a plain-English lesson, a type-it-yourself walkthrough inside a live Desmos calculator, and a 100-question drill bank that deals ten fresh questions per round. The first two modules — plus the 12-question diagnostic — are free.