Solve equations
Solve “mirror” systems where x and y coefficients are swapped
Standard elimination ignores the symmetry that lets you solve with one add and one subtract.
Spot it when
The system looks like ax+by=p and bx+ay=q (coefficients mirrored).
Watch it solved
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!
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A café sells 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.
An exam system is deliberately symmetric; spotting it saves the whole elimination grind.
Add and subtract the pair → x = 5, y = 2 in two moves.
A class drill on simultaneous equations is full of mirrored coefficients to train the eye.
Always: sum gives x+y, difference gives x−y, then halve.
The method behind it
संकलन-व्यवकलनाभ्याम्
Saṅkalana-vyavakalanābhyāṃ
“By addition and subtraction”
Add the two equations to get one answer; subtract them to get another. Two equations → two answers in two steps.
6 algebraic steps.
2 additions/subtractions + 2 divisions.
Use when
- • Equations of form ax+by=p and bx+ay=q
Avoid when
- • Non-symmetric systems