Apps

TalentJR apps

How the apps work →
Vedic maths · trick 34 of 36 · free

Simultaneous equations — Vedic maths trick

Two equations, two unknowns. A cross-multiplication pattern gives x and y directly, and when the numbers swap places the sutra “by addition and by subtraction” (Sankalana-Vyavakalanabhyam) is even faster.

▶ Watch how it works

Got it? Practise ↓

The trick

Paravartya Yojayet — “transpose and apply”

  1. For ax + by = c and dx + ey = f: bottom = a×e − b×d.
  2. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom.
  3. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve.
  4. Check your x and y in the first equation.

Use it for: Linear equations in two variables (Class 8–10). Type the answer as x and y in the two boxes.

Worked example: 2x + 3y = 13 and 5x − y = 7 → x = 2, y = 3

  1. Bottom: 2 × (−1) − 3 × 5 = −17.
  2. x = (13 × (−1) − 3 × 7) ÷ (−17) = −34 ÷ (−17) = 2.
  3. y = (2 × 7 − 13 × 5) ÷ (−17) = −51 ÷ (−17) = 3.
  4. Answer: x = 2, y = 3.

Check: 2 × 2 + 3 × 3 = 13 and 5 × 2 − 3 = 7 ✓

▶ Watch it animated

✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

✏️ Practice

Work it out in your head or on paper, then tap your answer — or type it and press Check. Stuck? Press “Show me how”.

Right: 0 · Tried: 0

🏁 Trick 34 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the ⚖️ Equation Solver badge when you pass — and a certificate when you finish all 6 tricks of Part 4 · Algebra & number sense. You can still take the test without signing in.

🖨️ Simultaneous Equations Worksheet

✨ Free AI tutor

Ask the AI tutor about this trick

Why does it work? When should you use it? Ask in English, मराठी or हिंदी.

Sign in with Google to ask Free — 20 questions a day.

👩‍🏫 Vedic maths classes — live online, request a call back

Prefer a real teacher? TalentJR teachers take live online classes anywhere in India. Tell us what you need and our team will call you with timings and fees.

Live online classesSmall groups or 1:1 with a teacher, from home, any city.
We call you backOur team asks what your child needs, then shares timings and fees.
Home tutor?We are still building our list of home tutors — ask on the call if there is one near you.
Badges, certificates & gifts A badge for every trick you pass, a certificate for every part you finish, plus TalentJR Points for daily practice. Abacus course Younger child? Start with the free abacus course (ages 5–14).