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.
✓ You passed this trick’s test.
The trick
Paravartya Yojayet — “transpose and apply”
For ax + by = c and dx + ey = f: bottom = a×e − b×d.
x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom.
Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve.
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
Work it out in your head or on paper, type the answer 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.
👩🏫 Vedic maths classes near you — online or at home
Prefer a real teacher? TalentJR teachers take live online classes anywhere in India and visit homes in
selected cities. 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.
🏠Teacher at homeA TalentJR teacher visits your home (selected cities).
🏫At a centreClasses at a TalentJR partner centre near you, where available.
