संकलन-व्यवकलनाभ्याम्
Saṅkalana-vyavakalanābhyāṃ
"By addition and subtraction"
What this sutra solves
Solve “mirror” systems — where x and y coefficients are swapped — with one addition and one subtraction.
A café sells two combos: 2 sandwiches + 3 coffees = ₹9, and 3 sandwiches + 2 coffees = ₹11. Find each price.
Add → x+y=4; subtract → x−y=2; so x = ₹3, y = ₹1.
Two equations, two unknowns. Normally you would substitute and grind. But look at the coefficients first — that is where this sutra wins.
Read the two equations
Two equations, two unknowns. Normally you would substitute and grind. But look at the coefficients first — that is where this sutra wins.
⚡ Speed Advantage
See how few steps Vedic method needs!
Best for
- • Symmetric simultaneous equations
Use when
- • Equations of form ax+by=p and bx+ay=q
Avoid when
- • Non-symmetric systems
Intuition
Add the two equations to get one answer; subtract them to get another. Two equations → two answers in two steps.
Story Mode
The Mirror Equations
Some equation pairs are mirror images — swap x and y and you get the other. This symmetry is the key. Add the mirrors to find ; subtract them to find . Then arithmetic gives you each.
Vedic vs conventional
6 algebraic steps.
2 additions/subtractions + 2 divisions.
Applications
Symmetric simultaneous equations
Equations where swapping x and y gives the other equation.
Common Mistakes to Avoid
Adding when the pair should be subtracted
Wrong approach
Correct approach
Why this happens
💡 Students remember the addition part but skip the subtraction half of the method.
Forgetting to divide by the coefficient sum or difference
Wrong approach
Correct approach
Why this happens
💡 The symmetry makes the equations look simpler than they are, so the coefficient step gets skipped.
Why It Works
Use the symmetric pair:
Add the equations:
Subtract the equations:
Recover each variable:
If ax+by=p and bx+ay=q, then adding: . Subtracting: . Then x and y follow from .